Automorphic Forms and L-Functions for the Group GL(n,R) (Cambridge Studies in Advanced Mathematics)
Cambridge University Press, 11/26/2015
EAN 9781107565029, ISBN10: 1107565022
Paperback, 516 pages, 22.9 x 15.2 x 2.9 cm
Language: English
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Introduction
1. Discrete group actions
2. Invariant differential operators
3. Automorphic forms and L-functions for SL(2,Z)
4. Existence of Maass forms
5. Maass forms and Whittaker functions for SL(n,Z)
6. Automorphic forms and L-functions for SL(3,Z)
7. The Gelbert–Jacquet lift
8. Bounds for L-functions and Siegel zeros
9. The Godement–Jacquet L-function
10. Langlands Eisenstein series
11. Poincaré series and Kloosterman sums
12. Rankin–Selberg convolutions
13. Langlands conjectures
Appendix. The GL(n)pack manual
References.