The Rogers-Ramanujan continued fraction and a new Eisenstein series identity

Heng Huat Chan; Song Heng Chan; Zhi Guo Liu

doi:10.1016/j.jnt.2009.01.014

The Rogers-Ramanujan continued fraction and a new Eisenstein series identity

Heng Huat Chan
, Song Heng Chan
, Zhi Guo Liu^*

^*此作品的通讯作者

数学科学学院

National University of Singapore
Nanyang Technological University

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

With two elementary trigonometric sums and the Jacobi theta function θ₁, we provide a new proof of two Ramanujan's identities for the Rogers-Ramanujan continued fraction in his lost notebook. We further derive a new Eisenstein series identity associated with the Rogers-Ramanujan continued fraction.

源语言	英语
页（从-至）	1786-1797
页数	12
期刊	Journal of Number Theory
卷	129
期	7
DOI	https://doi.org/10.1016/j.jnt.2009.01.014
出版状态	已出版 - 7月 2009

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10.1016/j.jnt.2009.01.014

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title = "The Rogers-Ramanujan continued fraction and a new Eisenstein series identity",

abstract = "With two elementary trigonometric sums and the Jacobi theta function θ1, we provide a new proof of two Ramanujan's identities for the Rogers-Ramanujan continued fraction in his lost notebook. We further derive a new Eisenstein series identity associated with the Rogers-Ramanujan continued fraction.",

keywords = "Eisenstein series, Elliptic function, Rogers-Ramanujan's continued fraction, Theta function",

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

year = "2009",

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AU - Chan, Heng Huat

AU - Chan, Song Heng

AU - Liu, Zhi Guo

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Y1 - 2009/7

N2 - With two elementary trigonometric sums and the Jacobi theta function θ1, we provide a new proof of two Ramanujan's identities for the Rogers-Ramanujan continued fraction in his lost notebook. We further derive a new Eisenstein series identity associated with the Rogers-Ramanujan continued fraction.

AB - With two elementary trigonometric sums and the Jacobi theta function θ1, we provide a new proof of two Ramanujan's identities for the Rogers-Ramanujan continued fraction in his lost notebook. We further derive a new Eisenstein series identity associated with the Rogers-Ramanujan continued fraction.

KW - Eisenstein series

KW - Elliptic function

KW - Rogers-Ramanujan's continued fraction

KW - Theta function

UR - https://www.scopus.com/pages/publications/67349193239

U2 - 10.1016/j.jnt.2009.01.014

DO - 10.1016/j.jnt.2009.01.014

M3 - 文章

AN - SCOPUS:67349193239

SN - 0022-314X

VL - 129

SP - 1786

EP - 1797

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 7

ER -

The Rogers-Ramanujan continued fraction and a new Eisenstein series identity

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