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- Author: Armand Borel
- Pages: 208
- Language: English
- ISBN/ASIN: 521580498
- ISBN13: 9780521580496
- Upload date: 19-12-2016, 20:47
- Category: Mathematics

This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup ^D*G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G this is introduced in the last sections, making this connection explicit.

The topics treated include the construction of fundamental domains, the notion of automorphic form on ^D*GG and its relationship with the classical automorphic forms on X, Poincar series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2(^D*G/G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras.

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