A theta function identity of degree eight and Eisenstein series identities

Zhi Guo Liu

doi:10.1016/j.jnt.2012.06.007

A theta function identity of degree eight and Eisenstein series identities

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we prove a theta function identity of degree eight using the theory of elliptic theta functions and the method of asymptotic analysis. This identity allows us to derive some curious Eisenstein series identities. We prove a new addition formula for theta functions which allows us to give an extension of the Hirschhorn septuple product identity.

Original language	English
Pages (from-to)	2955-2966
Number of pages	12
Journal	Journal of Number Theory
Volume	132
Issue number	12
DOIs	https://doi.org/10.1016/j.jnt.2012.06.007
State	Published - Dec 2012

Keywords

Addition formula
Eisenstein series
Elliptic function
Entire function
Septuple product identity
Theta function

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10.1016/j.jnt.2012.06.007

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title = "A theta function identity of degree eight and Eisenstein series identities",

abstract = "In this paper we prove a theta function identity of degree eight using the theory of elliptic theta functions and the method of asymptotic analysis. This identity allows us to derive some curious Eisenstein series identities. We prove a new addition formula for theta functions which allows us to give an extension of the Hirschhorn septuple product identity.",

keywords = "Addition formula, Eisenstein series, Elliptic function, Entire function, Septuple product identity, Theta function",

author = "Liu, \{Zhi Guo\}",

year = "2012",

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doi = "10.1016/j.jnt.2012.06.007",

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T1 - A theta function identity of degree eight and Eisenstein series identities

AU - Liu, Zhi Guo

PY - 2012/12

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N2 - In this paper we prove a theta function identity of degree eight using the theory of elliptic theta functions and the method of asymptotic analysis. This identity allows us to derive some curious Eisenstein series identities. We prove a new addition formula for theta functions which allows us to give an extension of the Hirschhorn septuple product identity.

AB - In this paper we prove a theta function identity of degree eight using the theory of elliptic theta functions and the method of asymptotic analysis. This identity allows us to derive some curious Eisenstein series identities. We prove a new addition formula for theta functions which allows us to give an extension of the Hirschhorn septuple product identity.

KW - Addition formula

KW - Eisenstein series

KW - Elliptic function

KW - Entire function

KW - Septuple product identity

KW - Theta function

UR - https://www.scopus.com/pages/publications/84865639070

U2 - 10.1016/j.jnt.2012.06.007

DO - 10.1016/j.jnt.2012.06.007

M3 - 文章

AN - SCOPUS:84865639070

SN - 0022-314X

VL - 132

SP - 2955

EP - 2966

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 12

ER -

A theta function identity of degree eight and Eisenstein series identities

Abstract

Keywords

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