Duke Mathematical Journal

Elliptic factors of Selberg zeta functions

Masao Tsuzuki
Source: Duke Math. J. Volume 88, Number 1 (1997), 29-75.
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Primary Subjects: 11M36
Secondary Subjects: 11F72
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077241398
Mathematical Reviews number (MathSciNet): MR1448016
Zentralblatt MATH identifier: 0877.11033
Digital Object Identifier: doi:10.1215/S0012-7094-97-08802-5

References

[B] E. W. Barnes, On the theory of multiple gamma functions, Trans. Cambridge Philos. Soc. 19 (1904), 375–426.
[BaMo] D. Barbasch and H. Moscovici, $L^2$-index and the Selberg trace formula, J. Funct. Anal. 53 (1983), no. 2, 151–201.
Mathematical Reviews (MathSciNet): MR85j:58137
Zentralblatt MATH: 0537.58039
Digital Object Identifier: doi:10.1016/0022-1236(83)90050-2
[G1] R. Gangolli, Asymptotic behavior of spectra of compact quotients of certain symmetric spaces, Acta Math. 121 (1968), 151–192.
Mathematical Reviews (MathSciNet): MR39:360
Zentralblatt MATH: 0169.46004
Digital Object Identifier: doi:10.1007/BF02391912
[G2] R. Gangolli, Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one, Illinois J. Math. 21 (1977), no. 1, 1–41.
Mathematical Reviews (MathSciNet): MR58:5524
Zentralblatt MATH: 0354.33013
Project Euclid: euclid.ijm/1256049498
[G3] R. Gangolli, The length spectra of some compact manifolds of negative curvature, J. Differential Geom. 12 (1977), no. 3, 403–424.
Mathematical Reviews (MathSciNet): MR58:31311
Zentralblatt MATH: 0365.53016
Project Euclid: euclid.jdg/1214434092
[GWar] R. Gangolli and G. Warner, Zeta functions of Selberg's type for some noncompact quotients of symmetric spaces of rank one, Nagoya Math. J. 78 (1980), 1–44.
Mathematical Reviews (MathSciNet): MR82m:58049
Project Euclid: euclid.nmj/1118786087
[HP] R. Hotta and R. Parthasarathy, A geometric meaning of the multiplicity of integrable discrete classes in $L\sp2(\Gamma \backslash G)$, Osaka J. Math. 10 (1973), 211–234.
Mathematical Reviews (MathSciNet): MR49:3031
Zentralblatt MATH: 0337.22016
Project Euclid: euclid.ojm/1200694298
[JL] J. Jorgenson and S. Lang, On Cramér's theorem for general Euler products with functional equation, Math. Ann. 297 (1993), no. 3, 383–416.
Mathematical Reviews (MathSciNet): MR94k:11101
Zentralblatt MATH: 0789.11054
Digital Object Identifier: doi:10.1007/BF01459509
[Ko] S. Koyama, Determinant expression of Selberg zeta functions. II, Trans. Amer. Math. Soc. 329 (1992), no. 2, 755–772.
Mathematical Reviews (MathSciNet): MR93g:11053
Zentralblatt MATH: 0744.11030
Digital Object Identifier: doi:10.2307/2153962
[Ku1] N. Kurokawa, Parabolic components of zeta functions, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), no. 1, 21–24.
Mathematical Reviews (MathSciNet): MR89m:11052
Zentralblatt MATH: 0642.10028
Digital Object Identifier: doi:10.3792/pjaa.64.21
Project Euclid: euclid.pja/1195513438
[Ku2] N. Kurokawa, Multiple sine functions and Selberg zeta functions, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), no. 3, 61–64.
Mathematical Reviews (MathSciNet): MR92d:11094
Zentralblatt MATH: 0738.11041
Digital Object Identifier: doi:10.3792/pjaa.67.61
Project Euclid: euclid.pja/1195512182
[Ku3] N. Kurokawa, Lectures on multiple sine functions, University of Tokyo, 1991.
[Ku4] N. Kurokawa, Gamma factors and Plancherel measures, Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), no. 9, 256–260.
Mathematical Reviews (MathSciNet): MR94b:11044
Zentralblatt MATH: 0797.11053
Digital Object Identifier: doi:10.3792/pjaa.68.256
Project Euclid: euclid.pja/1195511631
[Ku5] N. Kurokawa, Multiple zeta functions: an example, Zeta functions in geometry (Tokyo, 1990), Adv. Stud. Pure Math., vol. 21, Kinokuniya, Tokyo, 1992, pp. 219–226.
Mathematical Reviews (MathSciNet): MR94f:11084
Zentralblatt MATH: 0795.11037
[M] Y. I. Manin, Lectures on zeta functions and motives (according to Deninger and Kurokawa), Columbia University Number Theory Seminar (New York, 1992), Astérisque, no. 228, 1995, 4, 121–163.
Mathematical Reviews (MathSciNet): MR96d:11076
Zentralblatt MATH: 0840.14001
[Mi] R. Miatello, The Minakshisundaram-Pleijel coefficients for the vector-valued heat kernel on compact locally symmetric spaces of negative curvature, Trans. Amer. Math. Soc. 260 (1980), no. 1, 1–33.
Mathematical Reviews (MathSciNet): MR81f:58033
Zentralblatt MATH: 0444.58015
Digital Object Identifier: doi:10.2307/1999874
[SWar] P. Sally and G. Warner, The Fourier transform on semisimple Lie groups of real rank one, Acta Math. 131 (1973), 1–26.
Mathematical Reviews (MathSciNet): MR56:8755
Zentralblatt MATH: 0305.43007
Digital Object Identifier: doi:10.1007/BF02392034
[Sa] P. Sarnak, Determinants of Laplacians, Comm. Math. Phys. 110 (1987), no. 1, 113–120.
Mathematical Reviews (MathSciNet): MR89e:58116
Zentralblatt MATH: 0618.10023
Digital Object Identifier: doi:10.1007/BF01209019
Project Euclid: euclid.cmp/1104159171
[Sel] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87.
Mathematical Reviews (MathSciNet): MR19,531g
Zentralblatt MATH: 0072.08201
[Vi] M. F. Vignéras, L'équation fonctionnelle de la fonction zêta de Selberg du groupe modulaire $\rm PSL(2,\,\bf Z)$, Journées Arithmétiques de Luminy (Colloq. Internat. CNRS, Centre Univ. Luminy, Luminy, 1978), Astérisque, vol. 61, Soc. Math. France, Paris, 1979, pp. 235–249.
Mathematical Reviews (MathSciNet): MR81f:10040
Zentralblatt MATH: 0401.10036
[Vo] A. Voros, Spectral functions, special functions and the Selberg zeta function, Comm. Math. Phys. 110 (1987), no. 3, 439–465.
Mathematical Reviews (MathSciNet): MR89b:58173
Zentralblatt MATH: 0631.10025
Digital Object Identifier: doi:10.1007/BF01212422
Project Euclid: euclid.cmp/1104159315
[Wi] F. L. Williams, A factorization of the Selberg zeta function attached to a rank $1$ space form, Manuscripta Math. 77 (1992), no. 1, 17–39.
Mathematical Reviews (MathSciNet): MR93j:58141
Zentralblatt MATH: 0789.22024
Digital Object Identifier: doi:10.1007/BF02567041
[War] G. Warner, Selberg's trace formula for nonuniform lattices: the $R$-rank one case, Studies in algebra and number theory, Adv. in Math. Suppl. Stud., vol. 6, Academic Press, New York, 1979, pp. 1–142.
Mathematical Reviews (MathSciNet): MR81f:10044
Zentralblatt MATH: 0466.10018

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