Modern analysis of automorphic forms by example, vol.1,2

Description

"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... 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.