Elliptic functions to the quintic base
type: Item
instance of: scholarly article
title: Elliptic functions to the quintic base
zbMATH Open document ID: 1117.33012
author: Heng Huat Chan
author: Zhi-Guo Liu
published in: Pacific Journal of Mathematics
publication date: 2007-07-20T00:00:00Z
review text: ``We study two elliptic functions to the quintic base and find two nonlinear second order differential equations satisfied by them. We then derive two recurrence relations involving certain Eisenstein series associated with the group \(\Gamma _0(5)\). These recurrence relations allow us to derive infinite families of identities involving Eisenstein series and Dedekind \(\eta \)-products. An imaginary transformation for one of the elliptic functions is also derived.''
reviewed by: Gabriele Nebe
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 5173469
zbMATH Keywords: Eisenstein series
zbMATH Keywords: elliptic functions
zbMATH Keywords: Dedekind eta function
MaRDI profile type: Publication
full work available at URL: pjm.2006.226.53
OpenAlex ID: W2004354355
DOI: 10.2140/PJM.2006.226.53
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description: scientific article; zbMATH DE number 5173469