Automorphic Forms on Sl2 (R)

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*G\G 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.

Author: Armand Borel
Publisher: Cambridge University Press
Published: 08/01/2008
Pages: 208
Binding Type: Paperback
Weight: 0.69lbs
Size: 9.02h x 5.98w x 0.48d
ISBN: 9780521072120

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