Eisenstein series identities involving the Borweins' cubic theta functions
type: Item
instance of: scholarly article
title: Eisenstein series identities involving the Borweins' cubic theta functions
zbMATH Open document ID: 1278.11049
DOI: 10.1155/2012/181264
author: Ernest X. W. Xia
author: Olivia X. M. Yao
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: Based on the theories of Ramanujan's elliptic functions and the \((p, k)\)-parametrization of theta functions due to \textit{A. Alaca} et al. [Acta Arith. 124, 177--195 (2006; Zbl 1127.11035), Int. Math. Forum 2, No. 1-4, 45--68 (2007; Zbl 1163.11003), J. Number Theory 124, No. 2, 491--510 (2007; Zbl 1169.11002)]. we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of the computer. Some of these identities were proved by \textit{Z.-G. Liu} [Ramanujan J. 4, No. 1, 43--50 (2000; Zbl 1012.11033)] based on the fundamental theory of elliptic functions and some of them may be new. One side of each identity involves Eisenstein series, the other products of the Borweins' cubic theta functions. As applications, we evaluate some convolution sums. These evaluations are different from the formulas given by Alaca et al. (loc. cit.).
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 6106133
MaRDI profile type: Publication
Wikidata QID: Q58905834
full work available at URL: https://doi.org/10.1155/2012/181264
OpenAlex ID: W2003347634
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DBLP publication ID: journals/jam/XiaY12
description: scientific article; zbMATH DE number 6106133