$p$-adic periods, $p$-adic $L$-functions, and the $p$-adic uniformization of Shimura curves
Massimo Bertolini and Henri Darmon
Source: Duke Math. J. Volume 98, Number 2
(1999), 305-334.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077228215
Mathematical Reviews number (MathSciNet): MR1695201
Zentralblatt MATH identifier: 01425221
Digital Object Identifier: doi:10.1215/S0012-7094-99-09809-5
References
[B-SDGP] Katia Barré-Sirieix, Guy Diaz, François Gramain, and Georges Philibert, Une preuve de la conjecture de Mahler-Manin, Invent. Math. 124 (1996), no. 1-3, 1–9.
Mathematical Reviews (MathSciNet): MR96j:11103
Zentralblatt MATH: 0853.11059
Digital Object Identifier: doi:10.1007/s002220050044
[BD1] M. Bertolini and H. Darmon, Heegner points on Mumford-Tate curves, Invent. Math. 126 (1996), no. 3, 413–456.
Mathematical Reviews (MathSciNet): MR97k:11100
Zentralblatt MATH: 0882.11034
Digital Object Identifier: doi:10.1007/s002220050105
[BD2] Massimo Bertolini and Henri Darmon, Heegner points, $p$-adic $L$-functions, and the Cerednik-Drinfeld uniformization, Invent. Math. 131 (1998), no. 3, 453–491.
Mathematical Reviews (MathSciNet): MR99f:11080
Zentralblatt MATH: 0899.11029
Digital Object Identifier: doi:10.1007/s002220050211
[Boi] X. Boichut, On the Mazur-Tate-Teitelbaum $p$-adic conjecture for elliptic curves with bad reduction at $p$, in preparation.
[BC] J.-F. Boutot and H. Carayol, Uniformisation $p$-adique des courbes de Shimura: les théorèmes de Čerednik et de Drinfeld, Astérisque (1991), no. 196-197, 7, 45–158 (1992), in Courbes modulaires et courbes de Shimura (Orsay, 1987/1988), Soc. Math. France, Marseille.
Mathematical Reviews (MathSciNet): MR93c:11041
Zentralblatt MATH: 0781.14010
[C] I. V. Čerednik, Uniformization of algebraic curves by discrete arithmetic subgroups of $\rm PGL\sb2(k\sbw)$ with compact quotient spaces, Mat. Sb. (N.S.) 100(142) (1976), no. 1, 59–88, 165, (in Russian); English trans. in Math. USSR-Sb. 29 (1976), 55–78.
Mathematical Reviews (MathSciNet): MR58:10909
[Dag] H. Daghigh, Modular forms, quaternion algebras, and special values of $L$-functions, Ph.D. thesis, McGill University, 1997.
[Dr] V. G. Drinfeld, Coverings of $p$-adic symmetric domains, Funkcional. Anal. i Priložen. 10 (1976), no. 2, 29–40.
Mathematical Reviews (MathSciNet): MR54:10281
Zentralblatt MATH: 0346.14010
[GvdP] Lothar Gerritzen and Marius van der Put, Schottky groups and Mumford curves, Lecture Notes in Mathematics, vol. 817, Springer, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR82j:10053
Zentralblatt MATH: 0442.14009
[GS] Ralph Greenberg and Glenn Stevens, $p$-adic $L$-functions and $p$-adic periods of modular forms, Invent. Math. 111 (1993), no. 2, 407–447.
Mathematical Reviews (MathSciNet): MR93m:11054
Zentralblatt MATH: 0778.11034
Digital Object Identifier: doi:10.1007/BF01231294
[Gr] Benedict H. Gross, Heights and the special values of $L$-series, Number theory (Montreal, Que., 1985) eds. H. Kisilevsky and J. Labute, CMS Conf. Proc., vol. 7, Amer. Math. Soc., Providence, RI, 1987, pp. 115–187.
Mathematical Reviews (MathSciNet): MR89c:11082
Zentralblatt MATH: 0623.10019
[GZ] Benedict H. Gross and Don B. Zagier, Heegner points and derivatives of $L$-series, Invent. Math. 84 (1986), no. 2, 225–320.
Mathematical Reviews (MathSciNet): MR87j:11057
Zentralblatt MATH: 0608.14019
Digital Object Identifier: doi:10.1007/BF01388809
[JL] H. Jacquet and R. P. Langlands, Automorphic forms on $\rm GL(2)$, Lecture Notes in Math., vol. 114, Springer-Verlag, Berlin, 1970.
Mathematical Reviews (MathSciNet): MR53:5481
Zentralblatt MATH: 0236.12010
[KKT] K. Kato, M. Kurihara, and Tsuji, forthcoming work.
[K1] Christoph Klingenberg, On $p$-adic $L$-functions of Mumford curves, $p$-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991) eds. B. Mazur and G. Stevens, Contemp. Math., vol. 165, Amer. Math. Soc., Providence, RI, 1994, pp. 277–315.
Mathematical Reviews (MathSciNet): MR95j:11058
Zentralblatt MATH: 0863.14014
[M] Y. I. Manin, $p$-adic automorphic functions, J. Soviet Math. 5 (1976), 279–333.
Zentralblatt MATH: 0375.14007
[MTT] B. Mazur, J. Tate, and J. Teitelbaum, On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986), no. 1, 1–48.
Mathematical Reviews (MathSciNet): MR87e:11076
Zentralblatt MATH: 0699.14028
Digital Object Identifier: doi:10.1007/BF01388731
[RT] Kenneth A. Ribet and Shuzo Takahashi, Parametrizations of elliptic curves by Shimura curves and by classical modular curves, Proc. Nat. Acad. Sci. U.S.A. 94 (1997), no. 21, 11110–11114.
Mathematical Reviews (MathSciNet): MR99e:11080
Zentralblatt MATH: 0897.11018
Digital Object Identifier: doi:10.1073/pnas.94.21.11110
JSTOR: links.jstor.org
[Sch] P. Schneider, Rigid-analytic $L$-transforms, Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), Lecture Notes in Math., vol. 1068, Springer, Berlin, 1984, pp. 216–230.
Mathematical Reviews (MathSciNet): MR86b:11043
Zentralblatt MATH: 0572.14014
[Se] Jean-Pierre Serre, Arbres, amalgames, $\rm SL\sb2$, Astérisque, vol. 46, Société Mathématique de France, Paris, 1977.
Mathematical Reviews (MathSciNet): MR57:16426
Zentralblatt MATH: 0369.20013
[Sh] Takuro Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58 (1975), 83–126.
Mathematical Reviews (MathSciNet): MR52:10603
Zentralblatt MATH: 0316.10016
Project Euclid: euclid.nmj/1118795445
[T] Jeremy T. Teitelbaum, Values of $p$-adic $L$-functions and a $p$-adic Poisson kernel, Invent. Math. 101 (1990), no. 2, 395–410.
Mathematical Reviews (MathSciNet): MR91m:11034
Zentralblatt MATH: 0731.11065
Digital Object Identifier: doi:10.1007/BF01231508
[Vi] Marie-France Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Mathematics, vol. 800, Springer, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR82i:12016
Zentralblatt MATH: 0422.12008
Duke Mathematical Journal
