eBook ISBN:  9781470467111 
Product Code:  CHEL/136.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
eBook ISBN:  9781470467111 
Product Code:  CHEL/136.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 

Book DetailsAMS Chelsea PublishingVolume: 136; 1991; 236 pp
Ramanujan occupies a unique place in analytic number theory. His formulas, identities, and calculations are still amazing threequarters of a century after his death. Many of his discoveries seem to have appeared as if from the ether. His mentor and primary collaborator was the famous G. H. Hardy. Here, Hardy collects twelve of his own lectures on topics stemming from Ramanujan's life and work. The topics include partitions, hypergeometric series, Ramanujan's \(\tau\)function and round numbers.
Hardy was the first to recognize the brilliance of Ramanujan's ideas. As one of the great mathematicians of the time, it is fascinating to read Hardy's accounts of their importance and influence. The book concludes with a chapter by chapter overview written by Bruce C. Berndt. In this overview, Berndt gives references to current literature, developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers.ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

RAMANUJAN

PREFACE

PREFACE TO THE FOURTH PRINTING

CONTENTS

I THE INDIAN MATHEMATICIAN RAMANUJAN

II RAMANUJAN AND THE THEORYOF PRIME NUMBERS

III ROUND NUMBERS

IV SOME MORE PROBLEMS OF THE ANALYTIC THEORY OF NUMBERS

V A LATTICEPOINT PROBLEM

VI RAMANUJAN’S WORK ON PARTITIONS

VII HYPERGEOMETRIC SERIES

VIII ASYMPTOTIC THEORY OF PARTITIONS

IX THE REPRESENTATION OF NUMBERS AS SUMS OF SQUARES

X RAMANUJAN’S FUNCTION r(n)

XI DEFINITE INTEGRALS

XII ELLIPTIC AND MODULAR FUNCTIONS

BIBLIOGRAPHY

COMMENTARY ON RAMANUJAN BY G. H. HARDY


Reviews

From the fact that practically all topics of analytic number theory are mentioned, briefly or extensively, in this book in connection with one or the other of Ramanujan's ideas, theorems, conjectures, we realize the farreaching influence which his work has had on presentday mathematics … the book is not only an homage to Ramanujan's genius; it is a survey of many branches of modern arithmetic and analysis and, altogether, a book which makes fascinating reading.
Hans Rademacher, Mathematical Reviews


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Ramanujan occupies a unique place in analytic number theory. His formulas, identities, and calculations are still amazing threequarters of a century after his death. Many of his discoveries seem to have appeared as if from the ether. His mentor and primary collaborator was the famous G. H. Hardy. Here, Hardy collects twelve of his own lectures on topics stemming from Ramanujan's life and work. The topics include partitions, hypergeometric series, Ramanujan's \(\tau\)function and round numbers.
Hardy was the first to recognize the brilliance of Ramanujan's ideas. As one of the great mathematicians of the time, it is fascinating to read Hardy's accounts of their importance and influence. The book concludes with a chapter by chapter overview written by Bruce C. Berndt. In this overview, Berndt gives references to current literature, developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers.
Graduate students and research mathematicians interested in number theory.

RAMANUJAN

PREFACE

PREFACE TO THE FOURTH PRINTING

CONTENTS

I THE INDIAN MATHEMATICIAN RAMANUJAN

II RAMANUJAN AND THE THEORYOF PRIME NUMBERS

III ROUND NUMBERS

IV SOME MORE PROBLEMS OF THE ANALYTIC THEORY OF NUMBERS

V A LATTICEPOINT PROBLEM

VI RAMANUJAN’S WORK ON PARTITIONS

VII HYPERGEOMETRIC SERIES

VIII ASYMPTOTIC THEORY OF PARTITIONS

IX THE REPRESENTATION OF NUMBERS AS SUMS OF SQUARES

X RAMANUJAN’S FUNCTION r(n)

XI DEFINITE INTEGRALS

XII ELLIPTIC AND MODULAR FUNCTIONS

BIBLIOGRAPHY

COMMENTARY ON RAMANUJAN BY G. H. HARDY

From the fact that practically all topics of analytic number theory are mentioned, briefly or extensively, in this book in connection with one or the other of Ramanujan's ideas, theorems, conjectures, we realize the farreaching influence which his work has had on presentday mathematics … the book is not only an homage to Ramanujan's genius; it is a survey of many branches of modern arithmetic and analysis and, altogether, a book which makes fascinating reading.
Hans Rademacher, Mathematical Reviews