Ramanujan's Theta Functions
| Autor: | Shaun Cooper |
|---|---|
| EAN: | 9783319561721 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 12.06.2017 |
| Kategorie: | |
| Schlagworte: | Euler's product Jacobi's inversion theorem Rogers-Ramanujan continued fraction Weierstrass functions elliptic functions hypergeometric modular transformations partitions |
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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.
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.
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