Tohoku Mathematical Journal Articles (Project Euclid)
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The latest articles from Tohoku Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 19 Apr 2011 09:33 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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$\boldsymbol{Q}$-factorial Gorenstein toric Fano varieties with large Picard number
http://projecteuclid.org/euclid.tmj/1270041023
<strong>Benjamin Nill</strong>, <strong>Mikkel Øbro</strong><p><strong>Source: </strong>Tohoku Math. J. (2), Volume 62, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
In dimension $d$, ${\boldsymbol Q}$-factorial Gorenstein toric Fano varieties with
Picard number $\rho_X$ correspond to simplicial reflexive polytopes with $\rho_X +
d$ vertices. Casagrande showed that any $d$-dimensional simplicial reflexive
polytope has at most $3 d$ and $3d-1$ vertices if $d$ is even and odd, respectively.
Moreover, for $d$ even there is up to unimodular equivalence only one such polytope
with $3 d$ vertices, corresponding to the product of $d/2$ copies of a del Pezzo
surface of degree six. In this paper we completely classify all $d$-dimensional
simplicial reflexive polytopes having $3d-1$ vertices, corresponding to
$d$-dimensional ${\boldsymbol Q}$-factorial Gorenstein toric Fano varieties with
Picard number $2d-1$. For $d$ even, there exist three such varieties, with two being
singular, while for $d > 1$ odd there exist precisely two, both being nonsingular
toric fiber bundles over the projective line. This generalizes recent work of the
second author.
</p>projecteuclid.org/euclid.tmj/1270041023_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTThree consecutive approximation coefficients: asymptotic frequencies in semi-regular caseshttps://projecteuclid.org/euclid.tmj/1527904823<strong>Jaap de Jonge</strong>, <strong>Cor Kraaikamp</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 285--317.</p><p><strong>Abstract:</strong><br/>
Denote by $p_n/q_n, n=1,2,3,\ldots,$ the sequence of continued fraction convergents of a real irrational number $x$. Define the sequence of approximation coefficients by $\theta_n(x):=q_n\left|q_nx-p_n\right|, n=1,2,3,\ldots$. In the case of regular continued fractions the six possible patterns of three consecutive approximation coefficients, such as $\theta_{n-1}<\theta_n<\theta_{n+1}$, occur for almost all $x$ with only two different asymptotic frequencies. In this paper it is shown how these asymptotic frequencies can be determined for two other semi-regular cases. It appears that the optimal continued fraction has a similar distribution of only two asymptotic frequencies, albeit with different values. The six different values that are found in the case of the nearest integer continued fraction will show to be closely related to those of the optimal continued fraction.
</p>projecteuclid.org/euclid.tmj/1527904823_20180601220029Fri, 01 Jun 2018 22:00 EDTModules of bilinear differential operators over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$https://projecteuclid.org/euclid.tmj/1527904824<strong>Taher Bichr</strong>, <strong>Jamel Boujelben</strong>, <strong>Khaled Tounsi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 319--338.</p><p><strong>Abstract:</strong><br/>
Let $\frak{F}_\lambda, \lambda\in \mathbb{C}$, be the space of tensor densities of degree $\lambda$ on the supercircle $S^{1|1}$. We consider the superspace $\mathfrak{D}_{\lambda_1,\lambda_2,\mu}$ of bilinear differential operators from $\frak{F}_{\lambda_1}\otimes\frak{F}_{\lambda_2}$ to $\frak{F}_{\mu}$ as a module over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$. We prove the existence and the uniqueness of a canonical conformally equivariant symbol map from $\mathfrak{D}_{\lambda_1,\lambda_2,\mu}^k$ to the corresponding space of symbols. An explicit expression of the associated quantization map is also given.
</p>projecteuclid.org/euclid.tmj/1527904824_20180601220029Fri, 01 Jun 2018 22:00 EDTOn a class of singular superlinear elliptic systems in a ballhttps://projecteuclid.org/euclid.tmj/1537495350<strong>Dang Dinh Hai</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 339--352.</p><p><strong>Abstract:</strong><br/>
We establish the existence of large positive radial solutions for the elliptic system $$ \left\{ \begin{array}{c} -\Delta u=\lambda f(v) \ \text{in} \ B\\ -\Delta v=\lambda g(u) \ \text{in} \ B\\ u=v=0 \ \text{on} \ \partial B \end{array} \right. $$ when the parameter $\lambda>0$ is small, where $B$ is the open unit ball $\mathbb{R}^N,N>2, f,g:(0,\infty) \rightarrow \mathbb{R}$ are possibly singular at 0 and $f(u) \sim u^p,g(v) \sim v^q$ at $\infty$ for some $p,q>0$ with $pq>1$. Our approach is based on fixed point theory in a cone.
</p>projecteuclid.org/euclid.tmj/1537495350_20180920220248Thu, 20 Sep 2018 22:02 EDTPolar foliations on quaternionic projective spaceshttps://projecteuclid.org/euclid.tmj/1537495351<strong>Miguel Domínguez-Vázquez</strong>, <strong>Claudio Gorodski</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 353--375.</p><p><strong>Abstract:</strong><br/>
We classify irreducible polar foliations of codimension $q$ on quaternionic projective spaces $\mathbb{H} P^n$, for all $(n,q)\neq(7,1)$. We prove that all irreducible polar foliations of any codimension (resp. of codimension one) on $\mathbb{H} P^n$ are homogeneous if and only if $n+1$ is a prime number (resp. $n$ is even or $n=1$). This shows the existence of inhomogeneous examples of codimension one and higher.
</p>projecteuclid.org/euclid.tmj/1537495351_20180920220248Thu, 20 Sep 2018 22:02 EDTAn elementary proof of Cohen-Gabber theorem in the equal characteristic $p>0$ casehttps://projecteuclid.org/euclid.tmj/1537495352<strong>Kazuhiko Kurano</strong>, <strong>Kazuma Shimomoto</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 377--389.</p><p><strong>Abstract:</strong><br/>
The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.
</p>projecteuclid.org/euclid.tmj/1537495352_20180920220248Thu, 20 Sep 2018 22:02 EDTThe isometry groups of compact manifolds with almost negative Ricci curvaturehttps://projecteuclid.org/euclid.tmj/1537495353<strong>Atsushi Katsuda</strong>, <strong>Takeshi Kobayashi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 391--400.</p><p><strong>Abstract:</strong><br/>
We estimate the order of isometry groups of compact Riemannian manifolds which have negative Ricci curvature except for small portions, in terms of geometric quantities.
</p>projecteuclid.org/euclid.tmj/1537495353_20180920220248Thu, 20 Sep 2018 22:02 EDTOn the rational cohomology of regular surfaces isogenous to a product of curves with $\chi(\mathcal{O}_S)=2$https://projecteuclid.org/euclid.tmj/1537495354<strong>Matteo A. Bonfanti</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 401--423.</p><p><strong>Abstract:</strong><br/>
Let $S$ be a surface isogenous to a product of curves of unmixed type. After presenting several results useful to study the cohomology of $S$ we prove a structure theorem for the cohomology of regular surfaces isogenous to a product of unmixed type with $\chi (\mathcal{O}_S)=2$. In particular we found two families of surfaces of general type with maximal Picard number.
</p>projecteuclid.org/euclid.tmj/1537495354_20180920220248Thu, 20 Sep 2018 22:02 EDTThe equivalence of weak and very weak supersolutions to the porous medium equationhttps://projecteuclid.org/euclid.tmj/1537495355<strong>Pekka Lehtelä</strong>, <strong>Teemu Lukkari</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 425--445.</p><p><strong>Abstract:</strong><br/>
We prove that various notions of supersolutions to the porous medium equation are equivalent under suitable conditions. More spesifically, we consider weak supersolutions, very weak supersolutions, and $m$-superporous functions defined via a comparison principle. The proofs are based on comparison principles and a Schwarz type alternating method, which are also interesting in their own right. Along the way, we show that Perron solutions with merely continuous boundary values are continuous up to the parabolic boundary of a sufficiently smooth space-time cylinder.
</p>projecteuclid.org/euclid.tmj/1537495355_20180920220248Thu, 20 Sep 2018 22:02 EDTDouble lines on quadric hypersurfaceshttps://projecteuclid.org/euclid.tmj/1537495356<strong>Edoardo Ballico</strong>, <strong>Sukmoon Huh</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 447--473.</p><p><strong>Abstract:</strong><br/>
We study double line structures in projective spaces and quadric hypersurfaces, and investigate the geometry of irreducible components of Hilbert scheme of curves and moduli of stable sheaves of pure dimension 1 on a smooth quadric threefold.
</p>projecteuclid.org/euclid.tmj/1537495356_20180920220248Thu, 20 Sep 2018 22:02 EDTParallel mean curvature tori in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$https://projecteuclid.org/euclid.tmj/1537495357<strong>Katsuei Kenmotsu</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 475--485.</p><p><strong>Abstract:</strong><br/>
We explicitly determine tori that have a parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane.
</p>projecteuclid.org/euclid.tmj/1537495357_20180920220248Thu, 20 Sep 2018 22:02 EDTPseudo-Hermitian manifolds with automorphism group of maximal dimensionhttps://projecteuclid.org/euclid.tmj/1546570822<strong>Jae-Cheon Joo</strong>, <strong>Kang-Hyurk Lee</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 487--510.</p><p><strong>Abstract:</strong><br/>
This paper concerns a local characterization of 5-dimensional pseudo-Hermitian manifolds with maximal automorphism group in the case the underlying almost CR structures are not integrable. We also present examples of globally homogeneous model of maximal dimensional automorphism group.
</p>projecteuclid.org/euclid.tmj/1546570822_20190103220047Thu, 03 Jan 2019 22:00 ESTOn the K-stability of Fano varieties and anticanonical divisorshttps://projecteuclid.org/euclid.tmj/1546570823<strong>Kento Fujita</strong>, <strong>Yuji Odaka</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 511--521.</p><p><strong>Abstract:</strong><br/>
We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical $\mathbb{Q}$-divisors. First, we propose a condition in terms of certain anti-canonical $\mathbb{Q}$-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least a sufficient condition and also related to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.
</p>projecteuclid.org/euclid.tmj/1546570823_20190103220047Thu, 03 Jan 2019 22:00 ESTThe structure of the space of polynomial solutions to the canonical central systems of differential equations on the block Heisenberg groups: A generalization of a theorem of Korányihttps://projecteuclid.org/euclid.tmj/1546570824<strong>Anthony C. Kable</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 523--545.</p><p><strong>Abstract:</strong><br/>
A result of Korányi that describes the structure of the space of polynomial solutions to the Heisenberg Laplacian operator is generalized to the canonical central systems on the block Heisenberg groups. These systems of differential operators generalize the Heisenberg Laplacian and, like it, admit large algebras of conformal symmetries. The main result implies that in most cases all polynomial solutions can be obtained from a single one by the repeated application of conformal symmetry operators.
</p>projecteuclid.org/euclid.tmj/1546570824_20190103220047Thu, 03 Jan 2019 22:00 EST$\sigma$-actions and symmetric triadshttps://projecteuclid.org/euclid.tmj/1546570825<strong>Osamu Ikawa</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 547--565.</p><p><strong>Abstract:</strong><br/>
For a given compact connected Lie group and an involution on it, we can define a hyperpolar action. We study the orbit space and the properties of each orbit of the action. The result is a natural extension of maximal torus theory.
</p>projecteuclid.org/euclid.tmj/1546570825_20190103220047Thu, 03 Jan 2019 22:00 ESTWavelets in weighted norm spaceshttps://projecteuclid.org/euclid.tmj/1546570826<strong>Kazaros S. Kazarian</strong>, <strong>Samvel S. Kazaryan</strong>, <strong>Angel San Antolín</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 567--605.</p><p><strong>Abstract:</strong><br/>
We give a complete characterization of the classes of weight functions for which the higher rank Haar wavelet systems are unconditional bases in weighted norm Lebesgue spaces. Particulary it follows that higher rank Haar wavelets are unconditional bases in the weighted norm spaces with weights which have strong zeros at some points. This shows that the class of weight functions for which higher rank Haar wavelets are unconditional bases is much richer than it was supposed.
</p>projecteuclid.org/euclid.tmj/1546570826_20190103220047Thu, 03 Jan 2019 22:00 ESTTeichmüller spaces and tame quasiconformal motionshttps://projecteuclid.org/euclid.tmj/1546570827<strong>Yunping Jiang</strong>, <strong>Sudeb Mitra</strong>, <strong>Hiroshige Shiga</strong>, <strong>Zhe Wang</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 607--631.</p><p><strong>Abstract:</strong><br/>
The concept of “quasiconformal motion” was first introduced by Sullivan and Thurston (in [24]). Theorem 3 of that paper asserted that any quasiconformal motion of a set in the sphere over an interval can be extended to the sphere. In this paper, we give a counter-example to that assertion. We introduce a new concept called “tame quasiconformal motion” and show that their assertion is true for tame quasiconformal motions. We prove a much more general result that, any tame quasiconformal motion of a closed set in the sphere, over a simply connected Hausdorff space, can be extended as a quasiconformal motion of the sphere. Furthermore, we show that this extension can be done in a conformally natural way. The fundamental idea is to show that the Teichmüller space of a closed set in the sphere is a “universal parameter space” for tame quasiconformal motions of that set over a simply connected Hausdorff space.
</p>projecteuclid.org/euclid.tmj/1546570827_20190103220047Thu, 03 Jan 2019 22:00 ESTLarge deviations for continuous additive functionals of symmetric Markov processeshttps://projecteuclid.org/euclid.tmj/1546570828<strong>Seunghwan Yang</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 633--648.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a locally compact separable metric space and $m$ a positive Radon measure on $X$ with full topological support. Let ${\bf{M}}=(P_x,X_t)$ be an $m$-symmetric Markov process on $X$. Let $(\mathcal{E},\mathcal{D}(\mathcal{E}))$ be the Dirichlet form on $L^2(X;m)$ generated by ${\bf{M}}$. Let $\mu$ be a positive Radon measure in the Green-tight Kato class and $A^\mu_t$ the positive continuous additive functional in the Revuz correspondence to $\mu$. Under certain conditions, we establish the large deviation principle for positive continuous additive functionals $A^\mu_t$ of symmetric Markov processes.
</p>projecteuclid.org/euclid.tmj/1546570828_20190103220047Thu, 03 Jan 2019 22:00 ESTOrthogonality of divisorial Zariski decompositions for classes with volume zerohttps://projecteuclid.org/euclid.tmj/1552100439<strong>Valentino Tosatti</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 1--8.</p><p><strong>Abstract:</strong><br/>
We show that the orthogonality conjecture for divisorial Zariski decompositions on compact Kähler manifolds holds for pseudoeffective (1,1) classes with volume zero.
</p>projecteuclid.org/euclid.tmj/1552100439_20190308220117Fri, 08 Mar 2019 22:01 ESTInfinite particle systems of long range jumps with long range interactionshttps://projecteuclid.org/euclid.tmj/1552100440<strong>Syota Esaki</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 9--33.</p><p><strong>Abstract:</strong><br/>
In this paper a general theorem for constructing infinite particle systems of jump type with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction between particles is given by the logarithmic potential appearing random matrix theory or potentials of Ruelle's class with polynomial decay. It is shown that the system can be constructed for any $\alpha \in (0, 2)$ if its equilibrium measure $\mu$ is translation invariant, and $\alpha$ is restricted by the growth order of the 1-correlation function of the measure $\mu$ in general case.
</p>projecteuclid.org/euclid.tmj/1552100440_20190308220117Fri, 08 Mar 2019 22:01 ESTRational orbits of primitive trivectors in dimension sixhttps://projecteuclid.org/euclid.tmj/1552100441<strong>Akihiko Yukie</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 35--52.</p><p><strong>Abstract:</strong><br/>
Let $G=\operatorname{GL}(1)\times \mathrm{GSp}(6)$ and $V$ be the irreducible representation of $G$ of dimension 14 over a field of characteristic not equal to 2,3. This is an irreducible prehomogeneous vector space. We determine generic rational orbits and their stabilizers of this prehomogeneous vector space.
</p>projecteuclid.org/euclid.tmj/1552100441_20190308220117Fri, 08 Mar 2019 22:01 ESTObstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaceshttps://projecteuclid.org/euclid.tmj/1552100442<strong>Fumi-Yuki Maeda</strong>, <strong>Takao Ohno</strong>, <strong>Tetsu Shimomura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 53--68.</p><p><strong>Abstract:</strong><br/>
We introduce Musielak-Orlicz Newtonian space on a metric measure space. After discussing properties of weak upper gradients of functions in such spaces and Poincaré inequalities for functions with zero boundary values in bounded open subsets, we prove the existence and uniqueness of a solution to an obstacle problem for Musielak-Orlicz Dirichlet energy integral.
</p>projecteuclid.org/euclid.tmj/1552100442_20190308220117Fri, 08 Mar 2019 22:01 ESTRigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature boundhttps://projecteuclid.org/euclid.tmj/1552100443<strong>Yohei Sakurai</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 69--109.</p><p><strong>Abstract:</strong><br/>
We study Riemannian manifolds with boundary under a lower Bakry-Émery Ricci curvature bound. In our weighted setting, we prove several rigidity theorems for such manifolds with boundary. We conclude a rigidity theorem for the inscribed radii, a volume growth rigidity theorem for the metric neighborhoods of the boundaries, and various splitting theorems. We also obtain rigidity theorems for the smallest Dirichlet eigenvalues for the weighted $p$-Laplacians.
</p>projecteuclid.org/euclid.tmj/1552100443_20190308220117Fri, 08 Mar 2019 22:01 ESTThe $\boldsymbol{p}$-adic duality for the finite star-multiple polylogarithmshttps://projecteuclid.org/euclid.tmj/1552100444<strong>Shin-ichiro Seki</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 111--122.</p><p><strong>Abstract:</strong><br/>
We prove the $\boldsymbol{p}$-adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values.
</p>projecteuclid.org/euclid.tmj/1552100444_20190308220117Fri, 08 Mar 2019 22:01 ESTCharacterization of 2-dimensional normal Mather-Jacobian log canonical singularitieshttps://projecteuclid.org/euclid.tmj/1552100445<strong>Kohsuke Shibata</strong>, <strong>Nguyen Duc Tam</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 123--136.</p><p><strong>Abstract:</strong><br/>
In this paper we characterize 2-dimensional normal Mather-Jacobian log canonical singularities which are not complete intersections. We prove that a 2-dimensional normal singularity which is not a complete intersection is a Mather-Jacobian log canonical singularity if and only if it is a toric singularity with embedding dimension 4.
</p>projecteuclid.org/euclid.tmj/1552100445_20190308220117Fri, 08 Mar 2019 22:01 ESTToric Fano varieties associated to finite simple graphshttps://projecteuclid.org/euclid.tmj/1552100446<strong>Yusuke Suyama</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 137--144.</p><p><strong>Abstract:</strong><br/>
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.
</p>projecteuclid.org/euclid.tmj/1552100446_20190308220117Fri, 08 Mar 2019 22:01 ESTA generalized maximal diameter sphere theoremhttps://projecteuclid.org/euclid.tmj/1552100447<strong>Nathaphon Boonnam</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 145--155.</p><p><strong>Abstract:</strong><br/>
We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\widetilde M$ belonging to a certain class, then the diameter of $M$ does not exceed that of $\widetilde M$. Moreover, we prove that if the diameter of $M$ equals that of $\widetilde M$, then $M$ is isometric to the $n$-model of $\widetilde M$. The class of a two-sphere of revolution employed in our main theorem is very wide. For example, this class contains both ellipsoids of prolate type and spheres of constant sectional curvature. Thus our theorem contains both the maximal diameter sphere theorem proved by Toponogov [9] and the radial curvature version by the present author [2] as a corollary.
</p>projecteuclid.org/euclid.tmj/1552100447_20190308220117Fri, 08 Mar 2019 22:01 ESTClassification of biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in 7-dimensional Sasakian space formshttps://projecteuclid.org/euclid.tmj/1552100448<strong>Toru Sasahara</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 157--169.</p><p><strong>Abstract:</strong><br/>
In [5], D. Fetcu and C. Oniciuc presented the classification result for biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms. However, it is incomplete. In this paper, all such submanifolds are explicitly determined.
</p>projecteuclid.org/euclid.tmj/1552100448_20190308220117Fri, 08 Mar 2019 22:01 ESTCharacteristic cycles of highest weight Harish-Chandra modules and the Weyl group action on the conormal varietyhttps://projecteuclid.org/euclid.tmj/1561082595<strong>Leticia Barchini</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 171--205.</p><p><strong>Abstract:</strong><br/>
We give an inductive algorithm that computes the action of simple reflections on a subset of basis-vectors of the Borel-Moore homology of the conormal variety associated to the symmetric pair $(\text{Sp}(2n), \text{GL}(n))$.
</p>projecteuclid.org/euclid.tmj/1561082595_20190620220336Thu, 20 Jun 2019 22:03 EDTQuinary lattices and binary quaternion hermitian latticeshttps://projecteuclid.org/euclid.tmj/1561082596<strong>Tomoyoshi Ibukiyama</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 207--220.</p><p><strong>Abstract:</strong><br/>
In our previous papers, we defined the $G$-type number of any genera of quaternion hermitian lattices as a generalization of the type number of a quaternion algebra. Now we prove in this paper that the $G$-type number of any genus of positive definite binary quaternion hermitian maximal lattices in $B^2$ for a definite quaternion algebra $B$ over $\mathbb Q$ is equal to the class number of some explicitly defined genus of positive definite quinary quadratic lattices. This is a generalization of a part of the results in 1982, where only the principal genus was treated. Explicit formulas for this type number can be obtained by using Asai's class number formula. In particular, in case when the discriminant of $B$ is a prime, we will write down an explicit formula for $T$, $H$ and $2T-H$ for the non-principal genus, where $T$ and $H$ are the type number and the class number. This number was known for the principal genus before. In another paper, our new result is applied to polarized superspecial varieties and irreducible components of supersingular locus in the moduli of principally polarized abelian varieties having a model over a finite prime field, where $2T-H$ plays an important role.
</p>projecteuclid.org/euclid.tmj/1561082596_20190620220336Thu, 20 Jun 2019 22:03 EDTThe conservativeness of Girsanov transformed symmetric Markov processeshttps://projecteuclid.org/euclid.tmj/1561082597<strong>Yusuke Miura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 221--241.</p><p><strong>Abstract:</strong><br/>
In this paper, we study those Girsanov transformations of symmetric Markov processes which preserve the symmetry. Employing a criterion for uniform integrability of exponential martingales due to Chen [3], we identify the class of transformations which transform the original process into a conservative one, even if the original one is explosive. We also consider the class of transformations which transform to a recurrent one. In [14, 22], the same problems are studied for symmetric diffusion processes. Our main theorem is an extension of their results to symmetric Markov processes with jumps.
</p>projecteuclid.org/euclid.tmj/1561082597_20190620220336Thu, 20 Jun 2019 22:03 EDTSteady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitorhttps://projecteuclid.org/euclid.tmj/1561082598<strong>Ying Li</strong>, <strong>Anna Marciniak-Czochra</strong>, <strong>Izumi Takagi</strong>, <strong>Boying Wu</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 243--279.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a diffusion equation coupled to an ordinary differential equation with FitzHugh-Nagumo type nonlinearity. We construct continuous spatially heterogeneous steady states near, as well as far from, constant steady states and show that they are all unstable. In addition, we construct various types of steady states with jump discontinuities and prove that they are stable in a weak sense defined by Weinberger.The results are quite different from those for classical reaction-diffusion systems where all species diffuse.
</p>projecteuclid.org/euclid.tmj/1561082598_20190620220336Thu, 20 Jun 2019 22:03 EDTProducts of random walks on finite groups with moderate growthhttps://projecteuclid.org/euclid.tmj/1561082599<strong>Guan-Yu Chen</strong>, <strong>Takashi Kumagai</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 281--302.</p><p><strong>Abstract:</strong><br/>
In this article, we consider products of random walks on finite groups with moderate growth and discuss their cutoffs in the total variation. Based on several comparison techniques, we are able to identify the total variation cutoff of discrete time lazy random walks with the Hellinger distance cutoff of continuous time random walks. Along with the cutoff criterion for Laplace transforms, we derive a series of equivalent conditions on the existence of cutoffs, including the existence of pre-cutoffs, Peres' product condition and a formula generated by the graph diameters. For illustration, we consider products of Heisenberg groups and randomized products of finite cycles.
</p>projecteuclid.org/euclid.tmj/1561082599_20190620220336Thu, 20 Jun 2019 22:03 EDTA revisit on commutators of linear and bilinear fractional integral operatorhttps://projecteuclid.org/euclid.tmj/1561082600<strong>Mingming Cao</strong>, <strong>Qingying Xue</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 303--318.</p><p><strong>Abstract:</strong><br/>
Let $I_{\alpha}$ be the linear and $\mathcal{I}_{\alpha}$ be the bilinear fractional integral operators. In the linear setting, it is known that the two-weight inequality holds for the first order commutators of $I_{\alpha}$. But the method can't be used to obtain the two weighted norm inequality for the higher order commutators of $I_{\alpha}$. In this paper, using some known results, we first give an alternative simple proof for the first order commutators of $I_{\alpha}$. This new approach allows us to consider the higher order commutators. Then, by using the Cauchy integral theorem, we show that the two-weight inequality holds for the higher order commutators of $I_{\alpha}$. In the bilinear setting, we present a dyadic proof for the characterization between $BMO$ and the boundedness of $[b,\mathcal{I}_{\alpha}]$. Moreover, some bilinear paraproducts are also treated in order to obtain the boundedness of $[b,\mathcal{I}_{\alpha}]$.
</p>projecteuclid.org/euclid.tmj/1561082600_20190620220336Thu, 20 Jun 2019 22:03 EDTA flat projective variety with $D_8$-holonomyhttps://projecteuclid.org/euclid.tmj/1561082601<strong>Francis E. A. Johnson</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 319--326.</p><p><strong>Abstract:</strong><br/>
We show explicitly that the compact flat Kähler manifold of complex dimension three with $D_8$ holonomy studied by Dekimpe, Halenda and Szczepanski ([5] p. 367) possesses the structure of a nonsingular projective variety. This corrects a previous statement by H. Lange in [9] that the holonomy group of a hyperelliptic threefold is necessarily abelian.
</p>projecteuclid.org/euclid.tmj/1561082601_20190620220336Thu, 20 Jun 2019 22:03 EDTFibers of cyclic covering fibrations of a ruled surfacehttps://projecteuclid.org/euclid.tmj/1568772176<strong>Makoto Enokizono</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 3, 327--358.</p><p><strong>Abstract:</strong><br/>
We give an algorithm to classify singular fibers of finite cyclic covering fibrations of a ruled surface by using singularity diagrams. As the first application, we classify all fibers of 3-cyclic covering fibrations of genus 4 of a ruled surface and show that the signature of a complex surface with this fibration is non-positive by computing the local signature for any fiber. As the second application, we classify all fibers of hyperelliptic fibrations of genus 3 into 12 types according to the Horikawa index. We also prove that finite cyclic covering fibrations of a ruled surface have no multiple fibers if the degree of the covering is greater than 3.
</p>projecteuclid.org/euclid.tmj/1568772176_20190917220320Tue, 17 Sep 2019 22:03 EDTCancellation of fluctuation in stochastic ranking process with space-time dependent intensitieshttps://projecteuclid.org/euclid.tmj/1568772177<strong>Tetsuya Hattori</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 3, 359--396.</p><p><strong>Abstract:</strong><br/>
We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic distribution in the infinite particle limit. We assume topology of weak convergence for the space of distributions, which implies that the fluctuations among particles with different jump rates cancel in the limit. The results are proved by first finding an auxiliary stochastic ranking process, for which a strong law of large numbers is applied, and then applying a multi time recursive Gronwall's inequality. The limit has a representation in terms of non-Markovian processes which we call point processes with last-arrival-time dependent intensities. We also prove the propagation of chaos, i.e., the tagged particle processes also converge almost surely.
</p>projecteuclid.org/euclid.tmj/1568772177_20190917220320Tue, 17 Sep 2019 22:03 EDTExamples of austere orbits of the isotropy representations for semisimple pseudo-Riemannian symmetric spaceshttps://projecteuclid.org/euclid.tmj/1568772178<strong>Kurando Baba</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 3, 397--424.</p><p><strong>Abstract:</strong><br/>
Harvey-Lawson and Anciaux introduced the notion of austere submanifolds in pseudo-Riemannian geometry. We give an equivalent condition for an orbit of the isotropy representations for semisimple pseudo-Riemannian symmetric space to be an austere submanifold in a pseudo-sphere in terms of restricted root system theory with respect to Cartan subspaces. By using the condition we give examples of austere orbits.
</p>projecteuclid.org/euclid.tmj/1568772178_20190917220320Tue, 17 Sep 2019 22:03 EDTOn the curvature of the Fefferman metric of contact Riemannian manifoldshttps://projecteuclid.org/euclid.tmj/1568772179<strong>Masayoshi Nagase</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 3, 425--436.</p><p><strong>Abstract:</strong><br/>
It is known that a contact Riemannian manifold carries a generalized Fefferman metric on a circle bundle over the manifold. We compute the curvature of the metric explicitly in terms of a modified Tanno connection on the underlying manifold. In particular, we show that the scalar curvature descends to the pseudohermitian scalar curvature multiplied by a certain constant. This is an answer to a problem considered by Blair-Dragomir.
</p>projecteuclid.org/euclid.tmj/1568772179_20190917220320Tue, 17 Sep 2019 22:03 EDTPrimitive forms for affine cusp polynomialshttps://projecteuclid.org/euclid.tmj/1568772180<strong>Yoshihisa Ishibashi</strong>, <strong>Yuuki Shiraishi</strong>, <strong>Atsushi Takahashi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 3, 437--464.</p><p><strong>Abstract:</strong><br/>
We determine a primitive form for a universal unfolding of an affine cusp polynomial. Moreover, we prove that the resulting Frobenius manifold is isomorphic to the one constructed from the Gromov–Witten theory for an orbifold projective line with at most three orbifold points.
</p>projecteuclid.org/euclid.tmj/1568772180_20190917220320Tue, 17 Sep 2019 22:03 EDTLa version relative de la conjecture des périodes de Kontsevich-Zagier revisitéehttps://projecteuclid.org/euclid.tmj/1568772181<strong>Joseph Ayoub</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 3, 465--485.</p><p><strong>Abstract:</strong><br/>
In this short note, we remark that a small modification in the computation made in [5] of the algebra of the torsor of isomorphisms between the tangential Betti realisation and the De Rham realisation results in a statement of functional Kontsevich–Zagier type which is purely algebraic and much more satisfactory than the statement obtained in [5].
</p>projecteuclid.org/euclid.tmj/1568772181_20190917220320Tue, 17 Sep 2019 22:03 EDTQuasi-Galois points, I: Automorphism groups of plane curveshttps://projecteuclid.org/euclid.tmj/1576724789<strong>Satoru Fukasawa</strong>, <strong>Kei Miura</strong>, <strong>Takeshi Takahashi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 487--494.</p><p><strong>Abstract:</strong><br/>
We investigate the automorphism group of a plane curve, introducing the notion of a quasi-Galois point. We show that the automorphism group of several curves, for example, Klein quartic, Wiman sextic and Fermat curves, is generated by the groups associated with quasi-Galois points.
</p>projecteuclid.org/euclid.tmj/1576724789_20191218220742Wed, 18 Dec 2019 22:07 ESTRelative algebro-geometric stabilities of toric manifoldshttps://projecteuclid.org/euclid.tmj/1576724790<strong>Naoto Yotsutani</strong>, <strong>Bin Zhou</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 495--524.</p><p><strong>Abstract:</strong><br/>
In this paper we study the relative Chow and $K$-stability of toric manifolds. First, we give a criterion for relative $K$-stability and instability of toric Fano manifolds in the toric sense. The reduction of relative Chow stability on toric manifolds will be investigated using the Hibert-Mumford criterion in two ways. One is to consider the maximal torus action and its weight polytope. We obtain a reduction by the strategy of Ono [34], which fits into the relative GIT stability detected by Székelyhidi. The other way relies on $\mathbb{C}^*$-actions and Chow weights associated to toric degenerations following Donaldson and Ross-Thomas [13, 36]. In the end, we determine the relative $K$-stability of all toric Fano threefolds and present counter-examples which are relatively $K$-stable in the toric sense but which are asymptotically relatively Chow unstable.
</p>projecteuclid.org/euclid.tmj/1576724790_20191218220742Wed, 18 Dec 2019 22:07 ESTGeneralized Kähler Einstein metrics and uniform stability for toric Fano manifoldshttps://projecteuclid.org/euclid.tmj/1576724791<strong>Satoshi Nakamura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 525--532.</p><p><strong>Abstract:</strong><br/>
We give a complete criterion for the existence of generalized Kähler Einstein metrics on toric Fano manifolds from view points of a uniform stability in a sense of GIT and the properness of a functional on the space of Kähler metrics.
</p>projecteuclid.org/euclid.tmj/1576724791_20191218220742Wed, 18 Dec 2019 22:07 ESTCombinatorial Ricci curvature on cell-complex and Gauss-Bonnnet theoremhttps://projecteuclid.org/euclid.tmj/1576724792<strong>Kazuyoshi Watanabe</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 533--547.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce a new definition of the Ricci curvature on cell-complexes and prove the Gauss-Bonnnet type theorem for graphs and 2-complexes that decompose closed surfaces. The differential forms on a cell complex are defined as linear maps on the chain complex, and the Laplacian operates this differential forms. Our Ricci curvature is defined by the combinatorial Bochner-Weitzenböck formula. We prove some propositionerties of combinatorial vector fields on a cell complex.
</p>projecteuclid.org/euclid.tmj/1576724792_20191218220742Wed, 18 Dec 2019 22:07 ESTVanishing for Frobenius twists of ample vector bundleshttps://projecteuclid.org/euclid.tmj/1576724793<strong>Daniel Litt</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 549--557.</p><p><strong>Abstract:</strong><br/>
We prove several asymptotic vanishing theorems for Frobenius twists of ample vector bundles in positive characteristic. As an application, we improve the Bott-Danilov-Steenbrink vanishing theorem for ample vector bundles on toric varieties.
</p>projecteuclid.org/euclid.tmj/1576724793_20191218220742Wed, 18 Dec 2019 22:07 ESTA group-theoretic characterization of the Fock-Bargmann-Hartogs domainshttps://projecteuclid.org/euclid.tmj/1576724794<strong>Akio Kodama</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 559--580.</p><p><strong>Abstract:</strong><br/>
Let $M$ be a connected Stein manifold of dimension $N$ and let $D$ be a Fock-Bargmann-Hartogs domain in $\mathbb{C}^N$. Let $\mathrm{Aut}(M)$ and $\mathrm{Aut}(D)$ denote the groups of all biholomorphic automorphisms of $M$ and $D$, respectively, equipped with the compact-open topology. Note that $\mathrm{Aut}(M)$ cannot have the structure of a Lie group, in general; while it is known that $\mathrm{Aut}(D)$ has the structure of a connected Lie group. In this paper, we show that if the identity component of $\mathrm{Aut}(M)$ is isomorphic to $\mathrm{Aut}(D)$ as topological groups, then $M$ is biholomorphically equivalent to $D$. As a consequence of this, we obtain a fundamental result on the topological group structure of $\mathrm{Aut}(D)$.
</p>projecteuclid.org/euclid.tmj/1576724794_20191218220742Wed, 18 Dec 2019 22:07 EST$L^2$ curvature pinching theorems and vanishing theorems on complete Riemannian manifoldshttps://projecteuclid.org/euclid.tmj/1576724795<strong>Yuxin Dong</strong>, <strong>Hezi Lin</strong>, <strong>Shihshu Walter Wei</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 581--607.</p><p><strong>Abstract:</strong><br/>
In this paper, by using monotonicity formulas for vector bundle-valued $p$-forms satisfying the conservation law, we first obtain general $L^2$ global rigidity theorems for locally conformally flat (LCF) manifolds with constant scalar curvature, under curvature pinching conditions. Secondly, we prove vanishing results for $L^2$ and some non-$L^2$ harmonic $p$-forms on LCF manifolds, by assuming that the underlying manifolds satisfy pointwise or integral curvature conditions. Moreover, by a theorem of Li-Tam for harmonic functions, we show that the underlying manifold must have only one end. Finally, we obtain Liouville theorems for $p$-harmonic functions on LCF manifolds under pointwise Ricci curvature conditions.
</p>projecteuclid.org/euclid.tmj/1576724795_20191218220742Wed, 18 Dec 2019 22:07 ESTCompact double differences of composition operators on the Bergman spaces over the ballhttps://projecteuclid.org/euclid.tmj/1576724796<strong>Boo Rim Choe</strong>, <strong>Hyungwoon Koo</strong>, <strong>Jongho Yang</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 4, 609--637.</p><p><strong>Abstract:</strong><br/>
Choe et al. have recently characterized compact double differences formed by four composition operators acting on the standard weighted Bergman spaces over the disk of the complex plane. In this paper, we extend such a result to the ball setting. Our characterization is obtained under a suitable restriction on inducing maps, which is automatically satisfied in the case of the disk. We exhibit concrete examples, for the first time even for single composition operators, which shows that such a restriction is essential in the case of the ball.
</p>projecteuclid.org/euclid.tmj/1576724796_20191218220742Wed, 18 Dec 2019 22:07 ESTDynamical degree and arithmetic degree of endomorphisms on product varietieshttps://projecteuclid.org/euclid.tmj/1585101618<strong>Kaoru Sano</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 1--13.</p><p><strong>Abstract:</strong><br/>
For a dominant rational self-map on a smooth projective variety defined over a number field, Shu Kawaguchi and Joseph H. Silverman conjectured that the (first) dynamical degree is equal to the arithmetic degree at an algebraic point whose forward orbit is well-defined and Zariski dense. We give some examples of self-maps on product varieties and rational points on them for which the Kawaguchi-Silverman conjecture holds.
</p>projecteuclid.org/euclid.tmj/1585101618_20200324220036Tue, 24 Mar 2020 22:00 EDTHigher-order nonlinear Schrödinger equation in 2D casehttps://projecteuclid.org/euclid.tmj/1585101619<strong>Nakao Hayashi</strong>, <strong>Pavel I. Naumkin</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 15--37.</p><p><strong>Abstract:</strong><br/>
We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation in two dimensional case \[ \left\{\!\!\! \begin{array}{c} i\partial _{t}u+\frac{b}{2}\Delta u-\frac{1}{4}\Delta ^{2}u=\lambda \left\vert u\right\vert u,\text{ }t>0,\quad x\in \mathbb{R}^{2}\,\mathbf{,} \\ u\left( 0,x\right) =u_{0}\left( x\right) ,\quad x\in \mathbb{R}^{2} \,\mathbf{,} \end{array} \right. \] where $\lambda \in \mathbb{R}\mathbf{,}$ $b>0.$ We develop the factorization techniques for studying the large time asymptotics of solutions to the above Cauchy problem. We prove that the asymptotics has a modified character.
</p>projecteuclid.org/euclid.tmj/1585101619_20200324220036Tue, 24 Mar 2020 22:00 EDTRough integration via fractional calculushttps://projecteuclid.org/euclid.tmj/1585101620<strong>Yu Ito</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 39--62.</p><p><strong>Abstract:</strong><br/>
On the basis of fractional calculus, the author's previous study [9] introduced an approach to the integral of controlled paths against Hölder rough paths. The integral in [9] is defined by the Lebesgue integrals for fractional derivatives without using any arguments based on discrete approximation. In this paper, we revisit the approach of [9] and show that, for a suitable class of Hölder rough paths including geometric Hölder rough paths, the integral in [9] is consistent with that obtained by the usual integration theory of rough path analysis, given by the limit of the compensated Riemann–Stieltjes sums.
</p>projecteuclid.org/euclid.tmj/1585101620_20200324220036Tue, 24 Mar 2020 22:00 EDTOn étale fundamental groups of formal fibres of $p$-adic curveshttps://projecteuclid.org/euclid.tmj/1585101621<strong>Mohamed Saïdi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 63--76.</p><p><strong>Abstract:</strong><br/>
We investigate a certain class of (geometric) finite (Galois) coverings of formal fibres of $p$-adic curves and the corresponding quotient of the (geometric) étale fundamental group. A key result in our investigation is that these (Galois) coverings can be compactified to finite (Galois) coverings of proper $p$-adic curves. We also prove that the maximal prime-to-$p$ quotient of the geometric étale fundamental group of a (geometrically connected) formal fibre of a $p$-adic curve is (pro-)prime-to-$p$ free of finite computable rank .
</p>projecteuclid.org/euclid.tmj/1585101621_20200324220036Tue, 24 Mar 2020 22:00 EDTToric Fano contractions associated to long extremal rayshttps://projecteuclid.org/euclid.tmj/1585101622<strong>Osamu Fujino</strong>, <strong>Hiroshi Sato</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 77--86.</p><p><strong>Abstract:</strong><br/>
We show that a toric Fano contraction associated to an extremal ray whose length is greater than the dimension of its fiber is a projective space bundle.
</p>projecteuclid.org/euclid.tmj/1585101622_20200324220036Tue, 24 Mar 2020 22:00 EDTZeta-functions of root systems and Poincaré polynomials of Weyl groupshttps://projecteuclid.org/euclid.tmj/1585101623<strong>Yasushi Komori</strong>, <strong>Kohji Matsumoto</strong>, <strong>Hirofumi Tsumura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 87--126.</p><p><strong>Abstract:</strong><br/>
We consider a certain linear combination of zeta-functions of root systems for a root system. Showing two different expressions of this linear combination, we find that a certain signed sum of zeta-functions of root systems is equal to a sum involving Bernoulli functions of root systems. This identity gives a non-trivial functional relation among zeta-functions of root systems, if the signed sum does not identically vanish. This is a generalization of the authors' previous result (Proc. London Math. Soc. 100 (2010), 303–347). We present several explicit examples of such functional relations. We give a criterion of the non-vanishing of the signed sum, in terms of Poincaré polynomials of associated Weyl groups. Moreover we prove a certain converse theorem.
</p>projecteuclid.org/euclid.tmj/1585101623_20200324220036Tue, 24 Mar 2020 22:00 EDTSunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifoldshttps://projecteuclid.org/euclid.tmj/1585101624<strong>Carolyn Gordon</strong>, <strong>Eran Makover</strong>, <strong>Bjoern Muetzel</strong>, <strong>David Webb</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 127--147.</p><p><strong>Abstract:</strong><br/>
We give a general method for constructing compact Kähler manifolds $X_1$ and $X_2$ whose intermediate Jacobians $J^k(X_1)$ and $J^k(X_2)$ are isogenous for each $k$, and we exhibit some examples. The method is based upon the algebraic transplantation formalism arising from Sunada's technique for constructing pairs of compact Riemannian manifolds whose Laplace spectra are the same. We also show that the method produces compact Riemannian manifolds whose Lazzeri Jacobians are isogenous.
</p>projecteuclid.org/euclid.tmj/1585101624_20200324220036Tue, 24 Mar 2020 22:00 EDTNew functional equations of finite multiple polylogarithmshttps://projecteuclid.org/euclid.tmj/1585101625<strong>Masataka Ono</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 149--157.</p><p><strong>Abstract:</strong><br/>
We give a finite analogue of the well-known formula $\mathrm{Li}_{\underbrace{1, \ldots, 1}_n}(t)=\frac{1}{n!}\mathrm{Li}_1(t)^n$ of multiple polylogarithms for any positive integer $n$ by using the shuffle relation of finite multiple polylogarithms of Ono–Yamamoto type. Unlike the usual case, the terms regarded as error terms appear in this formula. As a corollary, we obtain “$t \leftrightarrow 1-t$” type new functional equations of finite multiple polylogarithms of Ono–Yamamoto type and Sakugawa-Seki type.
</p>projecteuclid.org/euclid.tmj/1585101625_20200324220036Tue, 24 Mar 2020 22:00 EDTErratum by Editorial office: Quasi-Galois points, I: Automorphism groups of plane curveshttps://projecteuclid.org/euclid.tmj/1585101626<strong>Satoru Fukasawa</strong>, <strong>Kei Miura</strong>, <strong>Takeshi Takahashi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 72, Number 1, 159--159.</p>projecteuclid.org/euclid.tmj/1585101626_20200324220036Tue, 24 Mar 2020 22:00 EDT