An entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students. The volume also contains many new results in the area. 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. Many of the ideas are incorporated into computer functions to allow the reader to explore them computationally.
An entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students. The volume also contains many new results in the area. 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. Many of the ideas are incorporated into computer functions to allow the reader to explore them computationally.
Dorian Goldfeld is a Professor in the Department of Mathematics at Columbia University
Inhaltsangabe
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.
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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