Read While You Wait - Get immediate ebook access, if available*, when you order a print book

Ramanujan's Theta Functions

Authors: Cooper, Shaun

Free Preview
  • 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
see more benefits

Buy this book

eBook $89.00
price for USA in USD (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 $169.99
price for USA in USD
  • ISBN 978-3-319-56171-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $119.99
price for USA in USD
  • ISBN 978-3-319-85843-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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.

Reviews

“Each chapter contains an extensive set of exercises, making the book suitable for students interested in an introduction to q-series, elliptic functions, and modular forms without necessarily requiring the theory of modular forms as a prerequisite. … it will be a valuable reference book on Ramanujan’s theta function identities together with their modern extensions and applications.” (Jeremy Lovejoy, Mathematical Reviews, April, 2018)
“This is a big and bountiful book, clearly written as a labor of love, and well worth the effort (both of writing and reading it). The book is pitched at advanced undergraduates, graduate students, and professionals or researchers, and this is entirely consonant with this kind of number theory … . It’s been a long time since I visited this material, but I am very happy to see it again.” (Michael Berg, MAA Reviews, November, 2017)

Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook $89.00
price for USA in USD (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 $169.99
price for USA in USD
  • ISBN 978-3-319-56171-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $119.99
price for USA in USD
  • ISBN 978-3-319-85843-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

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
Softcover ISBN
978-3-319-85843-2
Edition Number
1
Number of Pages
XVIII, 687
Number of Illustrations
1 b/w illustrations
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works are not included.