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

School of Mathematical Sciences

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

8 Scopus citations

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.

Original language	English
Pages (from-to)	1786-1797
Number of pages	12
Journal	Journal of Number Theory
Volume	129
Issue number	7
DOIs	https://doi.org/10.1016/j.jnt.2009.01.014
State	Published - Jul 2009

Keywords

Eisenstein series
Elliptic function
Rogers-Ramanujan's continued fraction
Theta function

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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

PY - 2009/7

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

Abstract

Keywords

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