Theta functions, elliptic functions and ?

by Heng Huat Chan

Overview

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.

Product Details

ISBN-13:	9783110540758
Publisher:	De Gruyter
Publication date:	07/06/2020
Series:	De Gruyter Textbook
Sold by:	Barnes & Noble
Format:	eBook
Pages:	138
File size:	15 MB
Note:	This product may take a few minutes to download.
Age Range:	18 Years

About the Author

Heng Huat Chan, National University of Singapore, Singapore.

Table of Contents

Introduction
Chapter 1. Euler's identities and Jacobi's triple product identity
Chapter 2. Jacobi's theta functions and Jacobi' triple product identity
Chapter 3. Generalization of Jacobi;'s theta functions
Chapter 4. Ramanujan's differential equations for Eisenstein series
Chapter 5. The Weierstrass elliptic functions
Chapter 6. Jacobi's elliptic functions
Chapter 7. Hypergeometric series
Chapter 8. Ramanujan's series for 1/π
Chapter 9. The Gauss-Brent-Salamin algorithm for π
References