Modular Forms with Integral and Half-Integral Weights

  • Xueli Wang
  • Dingyi Pei

Table of contents

  1. Front Matter
    Pages i-x
  2. Xueli Wang, Dingyi Pei
    Pages 1-11
  3. Xueli Wang, Dingyi Pei
    Pages 13-43
  4. Xueli Wang, Dingyi Pei
    Pages 45-64
  5. Xueli Wang, Dingyi Pei
    Pages 89-152
  6. Xueli Wang, Dingyi Pei
    Pages 153-204
  7. Xueli Wang, Dingyi Pei
    Pages 205-263
  8. Xueli Wang, Dingyi Pei
    Pages 265-319
  9. Xueli Wang, Dingyi Pei
    Pages 321-362
  10. Xueli Wang, Dingyi Pei
    Pages 363-429
  11. Back Matter
    Pages 431-432

About this book

Introduction

"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.

Keywords

Eisenstein series Half-integral weights Modular forms Quadratic forms

Authors and affiliations

  • Xueli Wang
    • 1
  • Dingyi Pei
    • 2
  1. 1.Department of MathematicsSouth China Normal UniversityGuangzhouChina
  2. 2.Institute of Mathematics and Information ScienceGuangzhou UniversityGuangzhouChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-29302-3
  • Copyright Information Science Press, Beijing and Springer Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-29301-6
  • Online ISBN 978-3-642-29302-3