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Hardcover ISBN:  9780821807774 
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Hardcover ISBN:  9780821807774 
Product Code:  GSM/17 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470420741 
Product Code:  GSM/17.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821807774 
eBook ISBN:  9781470420741 
Product Code:  GSM/17.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 

Book DetailsGraduate Studies in MathematicsVolume: 17; 1997; 259 ppMSC: Primary 32
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 thetafunctions and representations by quadratic forms.
ReadershipGraduate students and research mathematicians working in number theory and related topics of algebraic geometry.

Table of Contents

Chapters

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


Additional Material

Reviews

The author discusses many important topics in the theory of automorphic forms which are rarely seen in the textbooks available on the subject ... the presentation of the proofs ... is ... unusual, and this may give the reader a different flavor of the subject ... graduate students will certainly benefit from this book.
Mathematical Reviews 
An excellent place to begin the study of the analytic approach to modular forms ... a welcome addition to this growing expository of literature.
Bulletin of the AMS 
[T]his is an excellent book, requiring hard work from the reader and giving rich reward for her or his effort.
Zentralblatt MATH 
An excellent graduate text. The book by Iwaniec provides the graduate student and the researcher wishing to acquire the basics on automorphic forms with a beautifully written and selfcontained treatment of the classical modular and automorphic forms, Kloosterman sums, Hecke operators, automorphic Lfunctions, cusp forms and Eisenstein series, spherical functions, theta functions and convolution Lfunctions.
Bulletin of the London Mathematical Society


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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 thetafunctions and representations by quadratic forms.
Graduate students and research mathematicians working in number theory and related topics of algebraic geometry.

Chapters

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

The author discusses many important topics in the theory of automorphic forms which are rarely seen in the textbooks available on the subject ... the presentation of the proofs ... is ... unusual, and this may give the reader a different flavor of the subject ... graduate students will certainly benefit from this book.
Mathematical Reviews 
An excellent place to begin the study of the analytic approach to modular forms ... a welcome addition to this growing expository of literature.
Bulletin of the AMS 
[T]his is an excellent book, requiring hard work from the reader and giving rich reward for her or his effort.
Zentralblatt MATH 
An excellent graduate text. The book by Iwaniec provides the graduate student and the researcher wishing to acquire the basics on automorphic forms with a beautifully written and selfcontained treatment of the classical modular and automorphic forms, Kloosterman sums, Hecke operators, automorphic Lfunctions, cusp forms and Eisenstein series, spherical functions, theta functions and convolution Lfunctions.
Bulletin of the London Mathematical Society