Modern Analysis of Automorphic Forms By Example: Volume 1 (Cambridge Studies in Advanced Mathematics)
Cambridge University Press, 9/20/2018
EAN 9781107154001, ISBN10: 1107154006
Hardcover, 406 pages, 23.6 x 15.8 x 2.6 cm
Language: English
This is Volume 1 of a two-volume book that 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 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.
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.