Springer Monographs in Mathematics

Modular Forms: Basics and Beyond

Authors: Shimura, Goro

  • Contains advanced material but always reminds the reader of basic facts
  • Features the theory of modular forms of half-integral weight, and the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types
  • Discusses special values of various Dirichlet series associated to one or two modular forms
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Hardcover $139.00
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  • ISBN 978-1-4614-2124-5
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  • ISBN 978-1-4899-9355-7
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About this book

This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable.

One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes:

(I) The correspondence between the forms of half-integral weight and those of integral weight.

(II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight.

About the authors

Goro Shimura is currently a professor emeritus of mathematics at Princeton University.

Reviews

From the reviews:

“The book under review is a welcome addition to the existing literature on modular forms. Being written by one of the main contributors to this subject it is designed with great care and love to detailed proofs. … The book is complete in the sense that all statements are clearly formulated and proven in a very rigorous way. … use this book as a guided tour through much of Shimura’s work. Without any doubt this journey is rewarding.” (Stefan Kühnlein, Zentralblatt MATH, Vol. 1234, 2012)


Table of contents (5 chapters)

  • Preliminaries

    Shimura, Goro

    Pages 1-14

  • Theta Functions and Factors of Automorphy

    Shimura, Goro

    Pages 15-38

  • The Rationality and Eisenstein Series

    Shimura, Goro

    Pages 39-87

  • The Correspondence between Forms of Integral and Half-integral Weight

    Shimura, Goro

    Pages 89-127

  • The Arithmeticity of Critical Values of Dirichlet Series

    Shimura, Goro

    Pages 129-150

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-2125-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-2124-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4899-9355-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Modular Forms: Basics and Beyond
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-2125-2
DOI
10.1007/978-1-4614-2125-2
Hardcover ISBN
978-1-4614-2124-5
Softcover ISBN
978-1-4899-9355-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
X, 178
Topics