Spectral Methods of Automorphic Forms: Second Edition
About this Title
Henryk Iwaniec, Rutgers University, Piscataway, NJ
Publication: Graduate Studies in Mathematics
Publication Year 2002: Volume 53
ISBNs: 978-0-8218-3160-1 (print); 978-1-4704-1798-7 (online)
MathSciNet review: MR1942691
MSC: Primary 11F72; Secondary 11F12, 11F37
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style.
The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references.
Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues.
Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
Graduate students and researchers working in analytic number theory.
Table of Contents
- Chapter 0. Harmonic analysis on the Euclidean plane
- Chapter 1. Harmonic analysis on the hyperbolic plane
- Chapter 2. Fuchsian groups
- Chapter 3. Automorphic forms
- Chapter 4. The spectral theorem. Discrete part
- Chapter 5. The automorphic Green function
- Chapter 6. Analytic continuation of the Eisenstein series
- Chapter 7. The spectral theorem. Continuous part
- Chapter 8. Estimates for the Fourier coefficients of Maass forms
- Chapter 9. Spectral theory of Kloosterman sums
- Chapter 10. The trace formula
- Chapter 11. The distribution of eigenvalues
- Chapter 12. Hyperbolic lattice-point problems
- Chapter 13. Spectral bounds for cusp forms
- Appendix A. Classical analysis
- Appendix B. Special functions