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Automorphic Forms on SL2 (R) : Cambridge Tracts in Mathematics (Hardcover) - Armand Borel

Automorphic Forms on SL2 (R)

Cambridge Tracts in Mathematics (Hardcover)

Hardcover Published: 28th August 1997
ISBN: 9780521580496
Number Of Pages: 208

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This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2 or the upper-half plane X, with respect to a discrete subgroup 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 GG 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 (GG). 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. Graduate students and researchers in analytic number theory will find much to interest them in this book.

Industry Reviews

From the hardback review: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society From the hardback review: '... carefully and concisely written ... Clearly every mathematical library should have this book.' Zentralblatt

Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane
Prerequisites and notation
Review of SL2(R), differential operators, convolution
Action of G on X, discrete subgroups of G, fundamental domains
The unit disc model
Automorphic Forms and Cusp Forms
Growth conditions, automorphic forms
Poincare series
Constant term:the fundamental estimate
Finite dimensionality of the space of automorphic forms of a given type
Convolution operators on cuspidal functions
Eisenstein Series
Definition and convergence of Eisenstein series
Analytic continuation of the Eisenstein series
Eisenstein series and automorphic forms orthogonal to cusp forms
Spectral Decomposition and Representations
Spectral decomposition of L2(G G)m with respect to C
Generalities on representations of G
Representations of SL2(R)
Spectral decomposition of L2(G SL2(R)):the discrete spectrum
Spectral decomposition of L2(G SL2(R)): the continuous spectrum
Concluding remarks
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521580496
ISBN-10: 0521580498
Series: Cambridge Tracts in Mathematics (Hardcover)
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 208
Published: 28th August 1997
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.6
Weight (kg): 0.48