Main Automorphic forms on SL₂(R)
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Automorphic forms on SL₂(R)

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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
Request Code : ZLIBIO1288514
Categories:
Year:
1997
Edition:
First Edition
Publisher:
Cambridge University Press
Language:
English
Pages:
x, 192 p. ; 24 cm
ISBN 13:
0-521-58049-8
ISBN:
978-0-521-58049-6,0-521-58049-8,978-0-521-07212-0
Series:
Cambridge tracts in mathematics, 130

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