"The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. 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"--Publisher's description. Read more...
Abstract:
This is Volume 1 of a two-volume book that 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 for graduate students and researchers in automorphic forms, number theory, and other related fields. Read more...
Author(s): Garrett, Paul B
Series: Cambridge studies in advanced mathematics 173-174
Publisher: Cambridge University Press
Year: 2018
Language: English
Tags: Automorphic forms.;Forms (Mathematics);Automorphe Form;Analysis
Content: 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.
