Real quadratic double sums
arXiv:1502.01109 · doi:10.1016/j.indag.2015.06.002
Abstract
In 1988, Andrews, Dyson and Hickerson initiated the study of q-hypergeometric series whose coefficients are dictated by the arithmetic in real quadratic fields. In this paper, we provide a dozen q-hypergeometric double sums which are generating functions for the number of ideals of a given norm in rings of integers of real quadratic fields and prove some related identities.
18 pages, to appear in Indagationes Mathematicae