The Poisson kernel for Drinfeld modular curves
Author:
Jeremy T. Teitelbaum
Journal:
J. Amer. Math. Soc. 4 (1991), 491-511
MSC:
Primary 11G09; Secondary 11F85, 11R58
DOI:
https://doi.org/10.1090/S0894-0347-1991-1099281-6
MathSciNet review:
1099281
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References | Similar Articles | Additional Information
- J. L. Alperin, Local representation theory, Cambridge Studies in Advanced Mathematics, vol. 11, Cambridge University Press, Cambridge, 1986. Modular representations as an introduction to the local representation theory of finite groups. MR 860771
- V. G. Drinfel′d, Elliptic modules, Mat. Sb. (N.S.) 94(136) (1974), 594–627, 656 (Russian). MR 0384707
- Lothar Gerritzen and Marius van der Put, Schottky groups and Mumford curves, Lecture Notes in Mathematics, vol. 817, Springer, Berlin, 1980. MR 590243
- Ernst-Ulrich Gekeler, On the coefficients of Drinfel′d modular forms, Invent. Math. 93 (1988), no. 3, 667–700. MR 952287, DOI https://doi.org/10.1007/BF01410204
- Ernst-Ulrich Gekeler, Drinfel′d modular curves, Lecture Notes in Mathematics, vol. 1231, Springer-Verlag, Berlin, 1986. MR 874338
- David Goss, Modular forms for ${\bf F}_{r}[T]$, J. Reine Angew. Math. 317 (1980), 16–39. MR 581335, DOI https://doi.org/10.1515/crll.1980.317.16
- David Goss, $\pi $-adic Eisenstein series for function fields, Compositio Math. 41 (1980), no. 1, 3–38. MR 578049
- David Goss, On a new type of $L$-function for algebraic curves over finite fields, Pacific J. Math. 105 (1983), no. 1, 143–181. MR 688411
- N. J. Kuhn and S. A. Mitchell, The multiplicity of the Steinberg representation of ${\rm GL}_n{\bf F}_q$ in the symmetric algebra, Proc. Amer. Math. Soc. 96 (1986), no. 1, 1–6. MR 813797, DOI https://doi.org/10.1090/S0002-9939-1986-0813797-6
- Stephen A. Mitchell and Stewart B. Priddy, Stable splittings derived from the Steinberg module, Topology 22 (1983), no. 3, 285–298. MR 710102, DOI https://doi.org/10.1016/0040-9383%2883%2990014-9
- 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. MR 830037, DOI https://doi.org/10.1007/BF01388731
- P. Schneider, Rigid-analytic $L$-transforms, Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983) Lecture Notes in Math., vol. 1068, Springer, Berlin, 1984, pp. 216–230. MR 756097, DOI https://doi.org/10.1007/BFb0099455
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
- Jeremy T. Teitelbaum, Values of $p$-adic $L$-functions and a $p$-adic Poisson kernel, Invent. Math. 101 (1990), no. 2, 395–410. MR 1062968, DOI https://doi.org/10.1007/BF01231508
- Jeremy Teitelbaum, On Drinfel′d’s universal formal group over the $p$-adic upper half plane, Math. Ann. 284 (1989), no. 4, 647–674. MR 1006378, DOI https://doi.org/10.1007/BF01443357
- André Weil, On the analogue of the modular group in characteristic $p$, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 211–223. MR 0271030
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Article copyright:
© Copyright 1991
American Mathematical Society