Garrett Modern Analysis of Automorphic Forms By Example: Volume 1

Erscheinungsjahr 2018
ISBN: 978-1-108-22963-0
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 173, 0 Seiten

Reihe: Cambridge Studies in Advanced Mathematics

This 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, automorphic Plancherel theorem, and automorphic Green's functions. 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.

Autoren/Hrsg.

Garrett, Paul

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Garrett, Paul
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.