Atnaujinkite slapukų nuostatas

Modern Analysis of Automorphic Forms By Example 2 Hardback Book Set [Multiple-component retail product]

(University of Minnesota)
  • Formatas: Multiple-component retail product, 860 pages, aukštis x plotis x storis: 236x157x50 mm, weight: 1310 g, Worked examples or Exercises, Contains 2 hardbacks
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 20-Sep-2018
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1108697933
  • ISBN-13: 9781108697934
Kitos knygos pagal šią temą:
Modern Analysis of Automorphic Forms By Example 2 Hardback Book Set
  • Formatas: Multiple-component retail product, 860 pages, aukštis x plotis x storis: 236x157x50 mm, weight: 1310 g, Worked examples or Exercises, Contains 2 hardbacks
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 20-Sep-2018
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1108697933
  • ISBN-13: 9781108697934
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781108697934.html
This two-volume book provides a self-contained introduction to the analytical aspects of automorphic forms by proving several critical results carefully and in detail. With extensive examples, it will be useful text for graduate students and researchers working in automorphic forms, number theory, and other related fields.

This 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.

Recenzijos

'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

Daugiau informacijos

A two-volume self-contained introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
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.
Paul Garrett is Professor of Mathematics at the University of Minnesota. His research focuses on analytical issues in the theory of automorphic forms. He has published numerous journal articles as well as five books.