Theta Function In The Light Of Ramanujan
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Theta Function In The Light Of Ramanujan
Author: Mohamed Nishad Maniparambath
language: en
Publisher: LAP Lambert Academic Publishing
Release Date: 2014
This book is an introductory text on Theta function. It describes Classical Theta function, Ramanujan's Theta function and Cubic Theta function and Their developments and interconnection. This is designed for graduates and researchers as a start up material. The topics dealt with it includes Theta function as a solution of Heat conduction equation, elementary properties of Ramanujan's Theta function, One variable, Two variable, Three variable cubic theta functions and identities involving them.
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.
Number Theory in the Spirit of Ramanujan
Author: Bruce C. Berndt
language: en
Publisher: American Mathematical Soc.
Release Date: 2006
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.