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.

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.

In June 2009, a conference in number theory was held on the beautiful campus of Infosys in Bangalore. The impetus for organizing this meeting was to recognize and commemorate K. Venkatachaliengar, an outstanding, well-known mathematician, who taught primarily at universities in Bangalore and Mysore for most of his career. He was born on 8 December, 1908, and so the meeting marked the centenary of Venkatachaliengar's birth. In the last several decades of his long life of 95 years, KV, as he was affectionately known to most of his friends, had become keenly interested in the life and work of India's greatest mathematician, Srinivasa Ramanujan, and so it was natural for Ramanujan's first loves of theta functions, partitions, and q-series to be the focus of the conference. Accordingly, over 50 mathematicians gathered for the presentation of 32 lectures in memory of both Ramanujan and KV. This volume comprises 13 papers by mathematicians who lectured at the meeting. In addition, three papers on the life and work of KV, along with a complete list of his publications, are offered.

This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter.The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.