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2012 Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions
Ernest X. W. Xia, Olivia X. M. Yao
J. Appl. Math. 2012: 1-14 (2012). DOI: 10.1155/2012/181264


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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Ernest X. W. Xia. Olivia X. M. Yao. "Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions." J. Appl. Math. 2012 1 - 14, 2012.


Published: 2012
First available in Project Euclid: 2 January 2013

zbMATH: 1278.11049
MathSciNet: MR2979437
Digital Object Identifier: 10.1155/2012/181264

Rights: Copyright © 2012 Hindawi


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