Real quadratic double sums

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 r...

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Bibliographic Details
Published inIndagationes mathematicae Vol. 26; no. 4; pp. 697 - 712
Main Authors Lovejoy, Jeremy, Osburn, Robert
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2015
Subjects
[formula omitted]-series
Bailey pairs
Real quadratic fields
q-series
Bailey pairs
Real quadratic fields
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Summary: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.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2015.06.002