Automorphic Forms and L-Functions for the Group GL(n,R)

A self-contained graduate level introduction to the topic of L-functions, also containing new results.

Autorentext
Dorian Goldfeld is a Professor in the Department of Mathematics at Columbia University

Zusammenfassung
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 basic knowledge of classical analysis, complex variable theory, and algebra.

Inhalt
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.

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