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Introduction to Siegel Modular Forms and Dirichlet Series

  • Textbook
  • © 2009

Overview

Authors:
  1. Anatoli Andrianov

    1. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

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  • Will 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

Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Modular Forms

    • Anatoli Andrianov
    Pages 7-39

  3. Dirichlet Series of Modular Forms

    • Anatoli Andrianov
    Pages 41-62

  4. Hecke–Shimura Rings of Double Cosets

    • Anatoli Andrianov
    Pages 63-117

  5. Hecke Operators

    • Anatoli Andrianov
    Pages 119-136

  6. Euler Factorization of Radial Series

    • Anatoli Andrianov
    Pages 137-168

  7. Back Matter

    Pages 169-182
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Keywords

About this book

Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.

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)

Authors and Affiliations

  • Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

    Anatoli Andrianov

Bibliographic Information

  • Book Title: Introduction to Siegel Modular Forms and Dirichlet Series

  • Authors: Anatoli Andrianov

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-0-387-78753-4

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2009

  • Softcover ISBN: 978-0-387-78752-7Published: 22 December 2008

  • eBook ISBN: 978-0-387-78753-4Published: 17 March 2010

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 184

  • Topics: Number Theory, Algebra

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