**Translations of Mathematical Monographs**

1995;
334 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-1-4704-1868-7

Product Code: MMONO/145.S

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-4562-1
Product Code: MMONO/145.E**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

# Modular Forms and Hecke Operators

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*A. N. Andrianov; V. G. Zhuravlev*

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

#### Readership

Researchers and graduate students working in algebra and number theory.

#### Reviews & Endorsements

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

# Table of Contents

## Modular Forms and Hecke Operators

- Cover Cover11
- Titles in series i2
- Title page iii4
- Contents v6
- Introduction 110
- Chapter 1. Theta-series 312
- Chapter 2. Modular forms 4352
- Chapter 3. Hecke rings 93102
- Chapter 4. Hecke operators 225234
- Appendix 1. Symmetric matrices over a field 307316
- Appendix 2. Quadratic spaces 311320
- Appendix 3. Modules in quadratic fields and binary quadratic forms 321330
- Notes 325334
- References 329338
- List of notation 333342
- Back Cover Back Cover1345