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Topics in Classical Automorphic Forms
Henryk Iwaniec, Rutgers University, New Brunswick, NJ
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Graduate Studies in Mathematics
1997; 259 pp; hardcover
Volume: 17
ISBN-10: 0-8218-0777-3
ISBN-13: 978-0-8218-0777-4
List Price: US$47
Member Price: US$37.60
Order Code: GSM/17
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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 theta-functions and representations by quadratic forms.

Readership

Graduate students and research mathematicians working in number theory and related topics of algebraic geometry.

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 self-contained treatment of the classical modular and automorphic forms, Kloosterman sums, Hecke operators, automorphic L-functions, cusp forms and Eisenstein series, spherical functions, theta functions and convolution L-functions."

-- Bulletin of the London Mathematical Society

Table of Contents

  • Introduction
  • The classical modular forms
  • Automorphic forms in general
  • The Eisenstein and the Poincaré series
  • Kloosterman sums
  • Bounds for the Fourier coefficients of cusp forms
  • Hecke operators
  • Automorphic \(L\)-functions
  • Cusp forms associated with elliptic curves
  • Spherical functions
  • Theta functions
  • Representations by quadratic forms
  • Automorphic forms associated with number fields
  • Convolution \(L\)-functions
  • Bibliography
  • Index
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