Real quadratic double sums

Jeremy Lovejoy; Robert Osburn

doi:10.1016/j.indag.2015.06.002

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arXiv · 1502.01109

Real quadratic double sums

Jeremy Lovejoy·Robert Osburn

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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.

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Jeremy Lovejoy, Robert Osburn. 2015-02-04. Real quadratic double sums. https://doi.org/10.1016/j.indag.2015.06.002

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