Modern Analysis of Automorphic Forms by Example

ISBN-13: 9781107154001 / Angielski / Twarda / 2018 / 406 str.

Paul Garrett

Opis

A self-contained introduction to the analytical aspects of automorphic forms, with key proofs of critical results and extensive examples.

Recenzje

Review of Multi-volume Set: '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

Spis treści

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.