Ramanujan's Theta Functions

Authors: Cooper, Shaun

  • Contains a detailed and systematic analysis of theta functions, by level and by weight
  • Serves as a useful, encyclopedic reference, designed to be a full and comprehensive study of select levels of Theta functions and modular forms
  • Features topics that have been the subject of much recent research, with the material organized into a systematic setting
  • Marks the first time many of the topics within will have appeared in book form
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eBook 107,09 €
price for Spain (gross)
  • ISBN 978-3-319-56172-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-319-56171-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

About the authors

Shaun Cooper received a PhD in Mathematics from the University of Wisconsin at Madison in 1995 and has worked at Massey University in New Zealand ever since. He was a visiting Assistant Professor at the University of Minnesota for one semester in 2000, and has spent 12 months each at the National University of Singapore (2007/8) and the University of Newcastle, Australia (2015/16). He is the author of approximately 70 refereed journal articles and edited the book Development of Elliptic Functions According to Ramanujan.

Table of contents (15 chapters)

  • Sum to Product Identities

    Cooper, Shaun

    Pages 1-57

    Preview Buy Chapter 30,19 €
  • Elliptic Functions

    Cooper, Shaun

    Pages 59-128

    Preview Buy Chapter 30,19 €
  • Transformations

    Cooper, Shaun

    Pages 129-169

    Preview Buy Chapter 30,19 €
  • Theta Functions

    Cooper, Shaun

    Pages 171-242

    Preview Buy Chapter 30,19 €
  • Levels 1, 2, 3, and 4: Jacobi’s Inversion Theorem and Ramanujan’s Alternative Theories

    Cooper, Shaun

    Pages 243-293

    Preview Buy Chapter 30,19 €

Buy this book

eBook 107,09 €
price for Spain (gross)
  • ISBN 978-3-319-56172-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-319-56171-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Ramanujan's Theta Functions
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-56172-1
DOI
10.1007/978-3-319-56172-1
Hardcover ISBN
978-3-319-56171-4
Edition Number
1
Number of Pages
XVIII, 687
Number of Illustrations and Tables
1 b/w illustrations
Topics