Modern Analysis of Automorphic Forms By Example 2 Hardback Book Set
Modern Analysis of Automorphic Forms By Example 2 Hardback Book Set
£106.00
GBPThis two-volume book provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The featured critical results, which are proven carefully and in detail, include: discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem in Volume 1; and automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics in Volume 2. The book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.
- Provides an extensive and self-contained treatment of analytical aspects of automorphic forms
- Provides a deep exploration of three different examples with varying degrees of complexity and generality, allowing a gradual approach to multi-faceted and highly technical issues
- Collects the most important analytical ideas and proofs in the theory of automorphic forms
Reviews & endorsements
'Any researcher working in the analytic theory of automorphic forms on higher rank groups will want to own this book. It is a treasure trove of examples and proofs that are well known to experts but very difficult to find in the open literature.' Dorian Goldfeld, Columbia University, New York
'Written by a leading expert in the field, this volume provides a valuable account of the analytic theory of automorphic forms. The author chooses his examples to provide a middle road between the general theory and the most classical cases that do not exhibit all of the subject's more general phenomena. What makes this book special is this compromise and the subsequent aim, 'to discuss analytical issues at a technical level truly sufficient to convert appealing heuristics to persuasive, genuine proofs'.' John Friedlander, University of Toronto
'It is marvelous to see how Garrett goes about presenting such deep and broad material in what is certainly a superbly holistic manner. It's really a wonderful example of what I think is the right pedagogy for this part of number theory. The examples he uses are lynchpins for an increasingly elaborate development of the subject, and the reader has a number of accessible places to hang his hat as the story unfolds.' Michael Berg, MAA Reviews
Product details
November 2018Multiple copy pack
9781108697934
860 pages
236 × 157 × 50 mm
1.31kg
Temporarily unavailable - available from TBC
Table of Contents
- Volume 1:
- 1. Four small examples
- 2. The quotient Z+GL2(k)/GL2(A)
- 3. SL3(Z), SL5(Z)
- 4. Invariant differential operators
- 5. Integration on quotients
- 6. Action of G on function spaces on G
- 7. Discrete decomposition of cuspforms
- 8. Moderate growth functions, theory of the constant term
- 9. Unbounded operators on Hilbert spaces
- 10. Discrete decomposition of pseudo-cuspforms
- 11. Meromorphic continuation of Eisenstein series
- 12. Global automorphic Sobolev spaces, Green's functions
- 13. Examples – topologies on natural function spaces
- 14. Vector-valued integrals
- 15. Differentiable vector-valued functions
- 16. Asymptotic expansions. Volume 2:
- 1. Unbounded operators on Hilbert spaces
- 2. Discrete decomposition of pseudo-cuspforms
- 3. Meromorphic continuation of Eisenstein series
- 4. Global automorphic Sobolev spaces, Green's functions
- 5. Examples – topologies on natural function spaces
- 6. Vector-valued integrals
- 7. Differentiable vector-valued functions
- 8. Asymptotic expansions.
