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Theta functions, elliptic functions and π
-
Heng Huat Chan
Language:
English
Published/Copyright:
2020
About this book
This book presents several results on elliptic functions and Pi, using Jacobi’s triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan’s work on Pi. The included exercises make it ideal for both classroom use and self-study.
- A pedagogical presentation of elliptic functions, modular forms, and Ramanujan's work on Pi.
- Connects several parts of number theory through Jacobi’s triple product identity.
- Includes exercises, making it also suitable for self-study.
Author / Editor information
Heng Huat Chan, National University of Singapore, Singapore.
Topics
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Frontmatter
I -
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Contents
VII -
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Foreword
IX -
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Introduction
XI -
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Acknowledgments
XV -
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1 An introduction to Jacobi’s triple product identity
1 -
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2 Jacobi’s theta functions of one variable and the triple product identity
15 -
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3 Two-variable extensions of Jacobi’s theta functions and the partition function
29 -
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4 Ramanujan’s differential equations
41 -
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5 Elliptic functions and Jacobi’s triple product identity
53 -
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6 Two elliptic functions and their properties
63 -
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7 An elliptic function of Jacobi
75 -
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8 Hypergeometric series and Ramanujan’s series 1/π
87 -
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9 The Gauss–Brent–Salamin algorithm for π
103 -
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Index
117 -
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Bibliography
119
Publishing information
Pages and Images/Illustrations in book
eBook published on:
July 6, 2020
eBook ISBN:
9783110541915
Paperback published on:
July 6, 2020
Paperback ISBN:
9783110540710
Pages and Images/Illustrations in book
Front matter:
16
Main content:
122
Illustrations:
4
Audience(s) for this book
Students and lecturers in mathematics.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
