Topics in Classical Automorphic Forms (Graduate Studies in Mathematics, V. 17) (Graduate Studies in Mathematics, V. 17)

The book is based on the notes from the graduate course given by the author at Rutgers University in the fall of 1994 and the spring of 1995. The main goal of the book is to acquaint the reader with various perspectives of the theory of automorphic forms. In addition to detailed and often nonstandard exposition of familiar topics of the theory, particular attention is paid to such subjects as theta-functions and representations by quadratic forms. Chapter 0. Introduction Chapter 1. The Classical Modular Forms Chapter 2. Automorphic Forms In General Chapter 3. The Eisenstein And The Poincaré Series Chapter 4. Kloosterman Sums Chapter 5. Bounds For The Fourier Coefficients Of Cusp Forms Chapter 6. Hecke Operators Chapter 7. Automorphic $l$-functions Chapter 8. Cusp Forms Associated With Elliptic Curves Chapter 9. Spherical Functions Chapter 10. Theta Functions Chapter 11. Representations By Quadratic Forms Chapter 12. Automorphic Forms Associated With Number Fields Chapter 13. Convolution $l$-functions Henryk Iwaniec. Includes Bibliographical References And Index. The main purpose of the book is to present the reader with various perspectives of the theory of automorphic forms. In addition to detailed and often nonstandard exposition of familiar topics of the theory, with a particular emphasis on analytic aspects, special attention is paid to such subjects as theta-functions and representations of integers by quadratic forms. Aims to acquaint the reader with various perspectives of the theory of automorphic forms. This work focuses on such subjects as theta-functions and representations by quadratic forms.