eBook ISBN: | 978-1-4704-6711-1 |
Product Code: | CHEL/136.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $58.50 |
eBook ISBN: | 978-1-4704-6711-1 |
Product Code: | CHEL/136.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $58.50 |
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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 three-quarters 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developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers.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.
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Table of Contents
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RAMANUJAN
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PREFACE
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PREFACE TO THE FOURTH PRINTING
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CONTENTS
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I THE INDIAN MATHEMATICIAN RAMANUJAN
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II RAMANUJAN AND THE THEORYOF PRIME NUMBERS
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III ROUND NUMBERS
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IV SOME MORE PROBLEMS OF THE ANALYTIC THEORY OF NUMBERS
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V A LATTICE-POINT PROBLEM
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VI RAMANUJAN’S WORK ON PARTITIONS
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VII HYPERGEOMETRIC SERIES
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VIII ASYMPTOTIC THEORY OF PARTITIONS
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IX THE REPRESENTATION OF NUMBERS AS SUMS OF SQUARES
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X RAMANUJAN’S FUNCTION r(n)
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XI DEFINITE INTEGRALS
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XII ELLIPTIC AND MODULAR FUNCTIONS
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BIBLIOGRAPHY
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COMMENTARY ON RAMANUJAN BY G. H. HARDY
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Reviews
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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 far-reaching influence which his work has had on present-day 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 three-quarters 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 LATTICE-POINT PROBLEM
-
VI RAMANUJAN’S WORK ON PARTITIONS
-
VII HYPERGEOMETRIC SERIES
-
VIII ASYMPTOTIC THEORY OF PARTITIONS
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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 far-reaching influence which his work has had on present-day 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