Cubic theta functions
[摘要] Some new identities for the four cubic theta functions a'(q,z), a(q,z), b(q,z) and c(q,z) are given. For example, we show that a'(q,z)(3) = b(q,z)(3) + c(q)(2)c(q,z). This is a counterpart of the identity a(q,z)(3) = b(q)(2)b(q,z(3)) + c(q,z)(3), which was found by Hirschhorn et al. The Laurent series expansions of the four cubic theta functions are given. Their transformation properties are established using an elementary approach due to K. Venkatachaliengar. By applying the modular transformation to the identities given by Hirschhorn et al., several new identities in which a'(q,z) plays the role of a(q,z) are obtained. (C) 2003 Elsevier B.V. All rights reserved.
[发布日期] 2003-11-01 [发布机构]
[效力级别] Proceedings Paper [学科分类]
[关键词] cubic theta functions;modular transformation;Dedekind eta function [时效性]
