Automorphic Forms on SL2

✍ Scribed by Armand Borel

• Publisher: Cambridge University Press
• Year: 1997
• Tongue: English
• Leaves: 204
• Series: Cambridge Tracts in Mathematics
• Edition: First Edition
• Category: Library

✦ Synopsis

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 ^DG 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 ^DG\G and its relationship with the classical automorphic forms on X, Poincaré 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.