Overview
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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Table of contents (15 chapters)
Keywords
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.
Reviews
“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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Ramanujan's Theta Functions
Authors: Shaun Cooper
DOI: https://doi.org/10.1007/978-3-319-56172-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-56171-4Published: 26 June 2017
Softcover ISBN: 978-3-319-85843-2Published: 02 August 2018
eBook ISBN: 978-3-319-56172-1Published: 12 June 2017
Edition Number: 1
Number of Pages: XVIII, 687
Number of Illustrations: 1 b/w illustrations
Topics: Number Theory, Algebraic Geometry
Industry Sectors: IT & Software