Real quadratic double sums
Number Theory
2021-02-04 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1502.01109,
title = {Real quadratic double sums},
author = {Jeremy Lovejoy and Robert Osburn},
journal= {arXiv preprint arXiv:1502.01109},
year = {2021}
}
Comments
18 pages, to appear in Indagationes Mathematicae