Ramanujan's Theta Functions

  • Shaun Cooper

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Shaun Cooper
    Pages 1-57
  3. Shaun Cooper
    Pages 59-128
  4. Shaun Cooper
    Pages 129-169
  5. Shaun Cooper
    Pages 171-242
  6. Shaun Cooper
    Pages 423-466
  7. Shaun Cooper
    Pages 509-522
  8. Shaun Cooper
    Pages 523-551
  9. Shaun Cooper
    Pages 553-570
  10. Shaun Cooper
    Pages 571-593
  11. Shaun Cooper
    Pages 595-612
  12. Shaun Cooper
    Pages 613-666
  13. Back Matter
    Pages 667-687

About this book

Introduction

Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12.  Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research.

Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.

Keywords

elliptic functions hypergeometric modular transformations partitions Weierstrass functions Jacobi's inversion theorem Rogers-Ramanujan continued fraction Euler's product

Authors and affiliations

  • Shaun Cooper
    • 1
  1. 1.Institute of Natural and Mathematical SciencesMassey UniversityAucklandNew Zealand

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-56172-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56171-4
  • Online ISBN 978-3-319-56172-1
  • About this book