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

^*此作品的通讯作者

数学科学学院

National University of Singapore

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	53-64
页数	12
期刊	Pacific Journal of Mathematics
卷	226
期	1
DOI	https://doi.org/10.2140/pjm.2006.226.53
出版状态	已出版 - 7月 2006

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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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AU - Liu, Zhi Guo

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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

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Elliptic functions to the quintic base

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