Elliptic functions to the quintic base

Heng Huat Chan; Zhi Guo Liu

doi:10.2140/pjm.2006.226.53

Elliptic functions to the quintic base

Heng Huat Chan^*
, Zhi Guo Liu

^*Corresponding author for this work

School of Mathematical Sciences

National University of Singapore

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

9 Scopus citations

Abstract

We study two elliptic functions to the quintic base and find two nonlinearsecond order differential equations satisfied by them. We then derive tworecurrence relations involving certain Eisenstein series associated with thegroup Γ₀(5). These recurrence relations allow us to derive infinite familiesof identities involving the Eisenstein series and Dedekind η-products. Animaginary transformation for one of the elliptic functions is also derived.

Original language	English
Pages (from-to)	53-64
Number of pages	12
Journal	Pacific Journal of Mathematics
Volume	226
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2006.226.53
State	Published - Jul 2006

Keywords

Dedekind eta function
Eisenstein series
Elliptic functions

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10.2140/pjm.2006.226.53

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title = "Elliptic functions to the quintic base",

abstract = "We study two elliptic functions to the quintic base and find two nonlinearsecond order differential equations satisfied by them. We then derive tworecurrence relations involving certain Eisenstein series associated with thegroup Γ0(5). These recurrence relations allow us to derive infinite familiesof identities involving the Eisenstein series and Dedekind η-products. Animaginary transformation for one of the elliptic functions is also derived.",

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

year = "2006",

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AU - Chan, Heng Huat

AU - Liu, Zhi Guo

PY - 2006/7

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N2 - We study two elliptic functions to the quintic base and find two nonlinearsecond order differential equations satisfied by them. We then derive tworecurrence relations involving certain Eisenstein series associated with thegroup Γ0(5). These recurrence relations allow us to derive infinite familiesof identities involving the Eisenstein series and Dedekind η-products. Animaginary transformation for one of the elliptic functions is also derived.

AB - We study two elliptic functions to the quintic base and find two nonlinearsecond order differential equations satisfied by them. We then derive tworecurrence relations involving certain Eisenstein series associated with thegroup Γ0(5). These recurrence relations allow us to derive infinite familiesof identities involving the Eisenstein series and Dedekind η-products. Animaginary transformation for one of the elliptic functions is also derived.

KW - Dedekind eta function

KW - Eisenstein series

KW - Elliptic functions

UR - https://www.scopus.com/pages/publications/38549142517

U2 - 10.2140/pjm.2006.226.53

DO - 10.2140/pjm.2006.226.53

M3 - 文章

AN - SCOPUS:38549142517

SN - 0030-8730

VL - 226

SP - 53

EP - 64

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -

Elliptic functions to the quintic base

Abstract

Keywords

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