Softcover ISBN:  9780821841785 
Product Code:  STML/34 
List Price:  $41.00 
Individual Price:  $32.80 
Electronic ISBN:  9781470421458 
Product Code:  STML/34.E 
List Price:  $38.00 
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Book DetailsStudent Mathematical LibraryVolume: 34; 2006; 187 ppMSC: Primary 11; Secondary 33;
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.ReadershipUndergraduate and graduate students interested in number theory, including \(q\)series and theta functions.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Congruences for $p(n)$ and $\tau (n)$

Chapter 3. Sums of squares and sums of triangular numbers

Chapter 4. Eisenstein series

Chapter 5. The connection between hypergeometric functions and theta functions

Chapter 6. Applications of the primary theorem of Chapter 5

Chapter 7. The RogersRamanujan continued fraction


Additional Material

Reviews

... undergraduates will find no better place to meet the mind behind the towering reputation.
D. V. Feldman, University of New Hampshire for CHOICE Reviews 
This is a delightful little book on selected topics in number theory. ...I highly recommend this book to all mathematicians. It is a great resource both to learn from and to teach from. Even the experts will enjoy his new perspective on these old questions.
Journal of Approximation Theory 
This slender volume is extremely wellwritten and contains a wealth of material. It is a lucid and accessible introduction to a rich and fascinating area of mathematics, written by the world's leading expert. For anyone with a knowledge of calculus wanting to learn about the mathematical work of Ramanujan, this book is the best place to start.
Shaun Cooper, Massey University  New Zealand Newsletter 
...“Number theory in the spirit of Ramanujan” is a gem that deserves a place in every mathematician's library.
Zentralblatt MATH


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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.
Undergraduate and graduate students interested in number theory, including \(q\)series and theta functions.

Chapters

Chapter 1. Introduction

Chapter 2. Congruences for $p(n)$ and $\tau (n)$

Chapter 3. Sums of squares and sums of triangular numbers

Chapter 4. Eisenstein series

Chapter 5. The connection between hypergeometric functions and theta functions

Chapter 6. Applications of the primary theorem of Chapter 5

Chapter 7. The RogersRamanujan continued fraction

... undergraduates will find no better place to meet the mind behind the towering reputation.
D. V. Feldman, University of New Hampshire for CHOICE Reviews 
This is a delightful little book on selected topics in number theory. ...I highly recommend this book to all mathematicians. It is a great resource both to learn from and to teach from. Even the experts will enjoy his new perspective on these old questions.
Journal of Approximation Theory 
This slender volume is extremely wellwritten and contains a wealth of material. It is a lucid and accessible introduction to a rich and fascinating area of mathematics, written by the world's leading expert. For anyone with a knowledge of calculus wanting to learn about the mathematical work of Ramanujan, this book is the best place to start.
Shaun Cooper, Massey University  New Zealand Newsletter 
...“Number theory in the spirit of Ramanujan” is a gem that deserves a place in every mathematician's library.
Zentralblatt MATH