© 2009

Introduction to Siegel Modular Forms and Dirichlet Series


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 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.


Arithmetic algebra equation function number theory proof variable

Authors and affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesSt. PetersburgRussia

Bibliographic information

  • Book Title Introduction to Siegel Modular Forms and Dirichlet Series
  • Authors Anatoli Andrianov
  • Series Title Universitext
  • Series Abbreviated Title Universitext
  • DOI
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-0-387-78752-7
  • eBook ISBN 978-0-387-78753-4
  • Series ISSN 0172-5939
  • Edition Number 1
  • Number of Pages XII, 184
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


From the reviews:

"Introduction to Siegel Modular Forms and Dirichlet Series is a compact but masterful presentation of this important generalization of the classical theory, and a good deal more. … beneficiaries of this wonderful book are the obvious candidates: students of number theory with their qualifying examinations behind them, or very gifted undergraduates who have already learned group theory and complex analysis, some topology, some rings and fields, and so on." (Michael Berg, The Mathematical Association of America, May, 2009)

“Andrianov … offers a comparatively concrete, lowbrow treatment of Siegel modular forms, a large and important but still special class of higher-dimensional modular forms. Readers familiar with standard accounts of the one-dimensional story will find the flow and organization here comfortingly familiar … . Andrianov has suppressed entirely the vantage of algebraic geometry, presumably for simplicity. … Summing Up: Highly recommended. Upper-division undergraduate through professional collections.” (D. V. Feldman, Choice, Vol. 47 (4), December, 2009) “The book under review is a concise and self-contained introduction to the Hecke theory of Siegel modular forms and zeta functions and is suitable for beginners. … Siegel modular form is introduced and its analytic properties are investigated.” (Hidenori Katsurada, Mathematical Reviews, Issue 2010 f)