Introduction to Siegel Modular Forms and Dirichlet Series

  • Anatoli Andrianov

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Anatoli Andrianov
    Pages 7-39
  3. Anatoli Andrianov
    Pages 41-62
  4. Anatoli Andrianov
    Pages 63-117
  5. Anatoli Andrianov
    Pages 119-136
  6. Anatoli Andrianov
    Pages 137-168
  7. Back Matter
    Pages 169-182

About this book

Introduction

Introduction to Siegel Modular Forms and Dirichlet Series gives a concise and self-contained introduction to the multiplicative theory of Siegel modular forms, Hecke operators, and zeta functions, including the classical case of modular forms in one variable. It serves to attract young researchers to this beautiful field and makes the initial steps more pleasant. It treats a number of questions that are rarely mentioned in other books. It is the first and only book so far on Siegel modular forms that introduces such important topics as analytic continuation and the functional equation of spinor zeta functions of Siegel modular forms of genus two.

 

Unique features include:

* New, simplified approaches and a fresh outlook on classical problems

* The abstract theory of Hecke–Shimura rings for symplectic and related groups

* The action of Hecke operators on Siegel modular forms

* Applications of Hecke operators to a study of the multiplicative properties of Fourier coefficients of modular forms

* The proof of analytic continuation and the functional equation (under certain assumptions) for Euler products associated with modular forms of genus two

*Numerous exercises

 

Anatoli Andrianov is a leading researcher at the St. Petersburg branch of the Steklov Mathematical Institute of the Russian Academy of Sciences. He is well known for his works on the arithmetic theory of automorphic functions and quadratic forms, a topic on which he has lectured at many universities around the world.

Keywords

Arithmetic algebra equation function number theory proof variable

Authors and affiliations

  • Anatoli Andrianov
    • 1
  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesSt. PetersburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-78753-4
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-78752-7
  • Online ISBN 978-0-387-78753-4
  • Series Print ISSN 0172-5939
  • About this book