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^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	2955-2966
页数	12
期刊	Journal of Number Theory
卷	132
期	12
DOI	https://doi.org/10.1016/j.jnt.2012.06.007
出版状态	已出版 - 12月 2012

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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",

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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

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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

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