拉马努金笔记(第三卷)

拉马努金笔记(第三卷)
作 者: 布鲁斯 伯恩特
出版社: 哈尔滨工业大学出版社
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作者简介

暂缺《拉马努金笔记(第三卷)》作者简介

内容简介

During the years 1903-1914, Ramanujan recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, G. N. Watson and B. M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957.This book is the third offive volumes devoted to the editing of Ramanujan's notebooks. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan's quarterly reports. Part II, published in 1989, comprises accounts of Chapters 10-15 in Ramanujan's second notebook. In this volume, we examine Chapters 16-21 in the second notebook. For many of the results that are known, we provide references in the literature where proofs may be found. Otherwise, we give complete proofs. Most of the theorems in these six chapte...

图书目录

Preface

Introduction

CHAPTER 16

q-Series and Theta-Functions

CHAPTER 17

Fundamental Properties of Elliptic Functions

CHAPTER 18

The Jacobian Elliptic Functions

CHAPTER 19

Modular Equations of Degrees 3, 5, and 7 and Associated

Theta-Function Identities

CHAPTER 20

Modular Equations of Higher and Composite Degrees

CHAPTER 21

Eisenstein Series

References

Index

附录I 拉马努金的中国知音:数学家刘治国的“西天取经”之旅

附录II 刘治国教授访谈

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