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Ramanujan's Theta Functions

Shaun Cooper

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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Arithmetik, Algebra

Beschreibung

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.

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Schlagwörter

partitions, Rogers-Ramanujan continued fraction, hypergeometric modular transformations, elliptic functions, Euler's product, Jacobi's inversion theorem, Weierstrass functions