The Poisson kernel for Drinfeld modular curves

Teitelbaum, Jeremy T.

doi:10.1090/S0894-0347-1991-1099281-6

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
Full-text PDF Free Access

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