Modular Forms with Integral and Half-Integral Weights

Authors: Wang, Xueli, Pei, Dingyi

  • The first book available on modular forms dealing with integral and half-integral weights in a unified framework
  • The first book dealing with in detail Eisenstein series with half-integral weights
  • Includes all necessary basic material for reading modern research literature on modular forms with half-integral weights
  • Offers some very beautiful applications of modular forms of half-integral weights to some arithmetic problems of definite positive quadratic forms
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Hardcover $129.00
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About this book

"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics.

Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.

Reviews

From the book reviews:

“The book contains ten chapters. … this book is a welcome addition for the graduate student or the senior level undergraduate who is looking for a friendly introduction to the topic of modular forms. The book would be ideal for a one-term graduate course or an upper level undergraduate course.” (M. Ram Murty, Mathematical Reviews, May, 2014)

“The reader will find a thorough introduction to many central themes in the theory of modular forms of integral and half-integral weight in one variable. … This monograph is a very valuable addition to the literature on modular forms which will be useful for scholars and for graduate students in this very active branch of number theory.” (Günter Köhler, Zentralblatt MATH, Vol. 1263, 2013)

Table of contents (10 chapters)

  • Theta Functions and Their Transformation Formulae

    Wang, Xueli (et al.)

    Pages 1-11

  • Eisenstein Series

    Wang, Xueli (et al.)

    Pages 13-43

  • The Modular Group and Its Subgroups

    Wang, Xueli (et al.)

    Pages 45-64

  • Modular Forms with Integral Weight or Half-integral Weight

    Wang, Xueli (et al.)

    Pages 65-88

  • Operators on the Space of Modular Forms

    Wang, Xueli (et al.)

    Pages 89-152

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-29302-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-29301-6
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
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 with Integral and Half-Integral Weights
Authors
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Science Press, Beijing and Springer Berlin Heidelberg
Distribution Rights
Distribution rights in China: Science Press Ltd
eBook ISBN
978-3-642-29302-3
DOI
10.1007/978-3-642-29302-3
Hardcover ISBN
978-3-642-29301-6
Edition Number
1
Number of Pages
X, 432
Number of Illustrations and Tables
2 b/w illustrations
Topics