Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


$ p$-adic hyperbolic planes and modular forms

Author: John A. Rhodes
Journal: Trans. Amer. Math. Soc. 341 (1994), 469-504
MSC: Primary 11F41; Secondary 11F25, 11F85
MathSciNet review: 1159195
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For $ K$ a number field and $ {\mathbf{p}}$ a finite prime of $ K$, we define a $ {\mathbf{p}}$-adic hyperbolic plane and study its geometry under the action of $ G{L_2}({K_{\mathbf{p}}})$. Seeking an operator with properties analogous to those of the non-Euclidean Laplacian of the classical hyperbolic plane, we investigate the fundamental invariant integral operator, the Hecke operator $ {T_{\mathbf{p}}}$. Letting $ S$ be a finite set of primes of a totally real $ K$ (including all the infinite ones), a modular group $ \Gamma (S)$ is defined. This group acts discontinuously on a product of classical and $ {\mathbf{p}}$-adic hyperbolic planes. $ S$-modular forms and their associated Dirichlet series are studied.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11F41, 11F25, 11F85

Retrieve articles in all journals with MSC: 11F41, 11F25, 11F85

Additional Information

PII: S 0002-9947(1994)1159195-9
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia