Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions

Based on the theories of Ramanujan's elliptic functions and the (p, k)-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006) we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of the computer. Some of these identit...

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Bibliographic Details
Published inJournal of Applied Mathematics Vol. 2012; no. 2012; pp. 1097 - 1110-072
Main Authors Xia, Ernest X. W., Yao, Olivia X. M.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2012
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Convolution
Elliptic functions
Functional equations
Functions
Mathematical analysis
Mathematical models
Series
Studies
Sums
Theorems (Mathematics)
China
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Summary:Based on the theories of Ramanujan's elliptic functions and the (p, k)-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006) 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 Liu 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.
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ISSN:1110-757X
1687-0042
DOI:10.1155/2012/181264