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Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics) | 
 enlarge | Author: Armand Borel
Publisher: Cambridge University Press
Buy New: $92.40
New (18) Used (7) from $82.57
Media: Hardcover
Pages: 208
Number Of Items: 1
Shipping Weight (lbs): 1
Dimensions (in): 9.1 x 6.3 x 0.8
ISBN: 0521580498
Dewey Decimal Number: 515.9
EAN: 9780521580496
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Product Description
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, Poincare 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.
Book Description
The theory of automorphic forms, which goes back to the work of Poincare and Klein, has been considerably developed and generalized in the last 40 years by the use of new analytic methods, inspired in part by harmonic analysis on Lie groups. This book is devoted to the analytic theory of automorphic forms, limited to the case of fuchsian groups, but from those more general points of view.This first exposition of this approach in this special case should be accessible to researchers and graduate students having some familiarity with functional analysis and elementary Lie theory.
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