Journal of Applied Mathematics

Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions

Ernest X. W. Xia and Olivia X. M. Yao

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 181264, 14 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153502

Digital Object Identifier
doi:10.1155/2012/181264

Mathematical Reviews number (MathSciNet)
MR2979437

Zentralblatt MATH identifier
1278.11049

Citation

Xia, Ernest X. W.; Yao, Olivia X. M. Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions. J. Appl. Math. 2012 (2012), Article ID 181264, 14 pages. doi:10.1155/2012/181264. https://projecteuclid.org/euclid.jam/1357153502


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