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Families of Automorphic Forms (Modern Birkhauser Classics)

Families of Automorphic Forms (Modern Birkhauser Classics) Cover

 

Synopses & Reviews

Publisher Comments:

This book gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. These automorphic forms are allowed to have exponential growth at the cusps and singularities at other points as well. It is shown that the Poincaré series and Eisenstein series occur in families of automorphic forms of this general type. These families are meromorphic in the spectral parameter and the multiplier system jointly. The general part of the book closes with a study of the singularities of these families. The work is aimed primarily at mathematicians working on real analytic automorphic forms. However, the book will also encourage readers at the graduate level (already versed in the subject and in spectral theory of automorphic forms) to delve into the field more deeply. An introductory chapter explicates main ideas, and three concluding chapters are replete with examples that clarify the general theory and results developed therefrom. Reviews: "It is made abundantly clear that this viewpoint, of families of automorphic functions depending on varying eigenvalue and multiplier systems, is both deep and fruitful." - MathSciNet

Synopsis:

This text gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. It introduces the main ideas then offers many examples that clarify the general theory and results developed therefrom.

Table of Contents

Preface.- 1. Modular introduction.- I. General theory - 2. Universal covering group - 3. Discrete subgroups - 4. Automorphic forms - 5. Poincaré series - 6. Selfadjoint extension - 7. Families of automorphic forms - 8. Transformation and truncation - 9. Pseudo Casimir operator - 10. Meromorphic continuation - 11. Poincaré families along vertical lines - 12. Singularities of Poincaré families.- II. Examples - 13. Modular group - 14. Theta group - 15. Commutator subgroup.- References.

Product Details

ISBN:
9783034603355
Publisher:
Birkhauser
Location:
Basel
Author:
Bruggeman, Roelof W.
Subject:
Calculus
Subject:
Number Theory
Subject:
Mathematical Analysis
Subject:
Mathematics-Calculus
Subject:
Analytic automorphic forms
Subject:
Colin de Verdiere
Subject:
Discrete cofinite subgroups
Subject:
Eisenstein series.
Subject:
modular group
Subject:
Multiplier system
Subject:
Poincarâe series.
Subject:
Singularities
Subject:
Spectral theory
Subject:
Real functions
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Copyright:
Edition Description:
1st ed. 1994. 2nd printing
Series:
Modern Birkhäuser Classics
Publication Date:
20091123
Binding:
TRADE PAPER
Language:
English
Pages:
328
Dimensions:
235 x 155 mm 1020 gr

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Families of Automorphic Forms (Modern Birkhauser Classics)
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Product details 328 pages Birkhauser Basel - English 9783034603355 Reviews:
"Synopsis" by , This text gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. It introduces the main ideas then offers many examples that clarify the general theory and results developed therefrom.
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