Ramanujan’s Theta Functions

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.