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Modular Forms and Hecke Operators
A. N. Andrianov and V. G. Zhuravlev
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Translations of Mathematical Monographs
1995; 334 pp; hardcover
Volume: 145
ISBN-10: 0-8218-0277-1
ISBN-13: 978-0-8218-0277-9
List Price: US$129
Member Price: US$103.20
Order Code: MMONO/145
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The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms.

As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms.

Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results.

Features:

  • The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.
  • Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms.

It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.

Readership

Researchers and graduate students working in algebra and number theory.

Reviews

"Gives a comprehensive account of the theory of Hecke operators on Siegel modular forms, motivated by the applications to the theory of positive-definite quadratic forms. For those with this ... interest, it will be invaluable."

-- Bulletin of the London Mathematical Society

Table of Contents

  • Introduction
  • Theta-series
  • Modular forms
  • Hecke rings
  • Hecke operators
  • Symmetric matrices over a field
  • Quadratic spaces
  • Modules in quadratic fields and binary quadratic forms
  • Notes
  • References
  • List of notation
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