Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 181264, 14 pages.
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 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.
J. Appl. Math., Volume 2012 (2012), Article ID 181264, 14 pages.
First available in Project Euclid: 2 January 2013
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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