Universitext

Introduction to Siegel Modular Forms and Dirichlet Series

Authors: Andrianov, Anatoli

  • Set to become a standard reference on the subject
  • Intended for graduate students and keeps prerequisites to a minimum
  • Gives provocative examples in the simplest and most accessible terms
  • The author is an expert who has originated many important ideas in the subject
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eBook 34,99 €
price for Spain (gross)
  • ISBN 978-0-387-78753-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 44,67 €
price for Spain (gross)
  • ISBN 978-0-387-78752-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

Reviews

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)

Table of contents (5 chapters)

Buy this book

eBook 34,99 €
price for Spain (gross)
  • ISBN 978-0-387-78753-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 44,67 €
price for Spain (gross)
  • ISBN 978-0-387-78752-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Siegel Modular Forms and Dirichlet Series
Authors
Series Title
Universitext
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-78753-4
DOI
10.1007/978-0-387-78753-4
Softcover ISBN
978-0-387-78752-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 184
Topics