Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics, Book 130)
Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics, Book 130) by Armand Borel
English | 1997 | ISBN: 0521580498 | ISBN-13: 9780521580496 | 208 pages | PDF | 6,8 MB
English | 1997 | ISBN: 0521580498 | ISBN-13: 9780521580496 | 208 pages | PDF | 6,8 MB
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, 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.