On a new circular summation of theta functions

Song Heng Chan; Zhi Guo Liu

doi:10.1016/j.jnt.2009.09.011

On a new circular summation of theta functions

Song Heng Chan
, Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

Nanyang Technological University

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

16 Scopus citations

Abstract

In this paper, we prove a new formula for circular summation of theta functions, which greatly extends Ramanujan's circular summation of theta functions and a very recent result of Zeng. Some applications of this circular summation formula are given. Also, an imaginary transformation for multiple theta functions is derived.

Original language	English
Pages (from-to)	1190-1196
Number of pages	7
Journal	Journal of Number Theory
Volume	130
Issue number	5
DOIs	https://doi.org/10.1016/j.jnt.2009.09.011
State	Published - May 2010

Keywords

Addition formula
Circular summation
Elliptic function
Modular equation
Theta function

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10.1016/j.jnt.2009.09.011

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title = "On a new circular summation of theta functions",

abstract = "In this paper, we prove a new formula for circular summation of theta functions, which greatly extends Ramanujan's circular summation of theta functions and a very recent result of Zeng. Some applications of this circular summation formula are given. Also, an imaginary transformation for multiple theta functions is derived.",

keywords = "Addition formula, Circular summation, Elliptic function, Modular equation, Theta function",

author = "Chan, \{Song Heng\} and Liu, \{Zhi Guo\}",

year = "2010",

month = may,

doi = "10.1016/j.jnt.2009.09.011",

language = "英语",

volume = "130",

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T1 - On a new circular summation of theta functions

AU - Chan, Song Heng

AU - Liu, Zhi Guo

PY - 2010/5

Y1 - 2010/5

N2 - In this paper, we prove a new formula for circular summation of theta functions, which greatly extends Ramanujan's circular summation of theta functions and a very recent result of Zeng. Some applications of this circular summation formula are given. Also, an imaginary transformation for multiple theta functions is derived.

AB - In this paper, we prove a new formula for circular summation of theta functions, which greatly extends Ramanujan's circular summation of theta functions and a very recent result of Zeng. Some applications of this circular summation formula are given. Also, an imaginary transformation for multiple theta functions is derived.

KW - Addition formula

KW - Circular summation

KW - Elliptic function

KW - Modular equation

KW - Theta function

UR - https://www.scopus.com/pages/publications/77949872757

U2 - 10.1016/j.jnt.2009.09.011

DO - 10.1016/j.jnt.2009.09.011

M3 - 文章

AN - SCOPUS:77949872757

SN - 0022-314X

VL - 130

SP - 1190

EP - 1196

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 5

ER -

On a new circular summation of theta functions

Abstract

Keywords

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