Multiplicative 𝑞-hypergeometric series arising from real quadratic fields

Bringmann, Kathrin; Kane, Ben

doi:10.1090/S0002-9947-2010-05214-6

Multiplicative $q$-hypergeometric series arising from real quadratic fields
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by Kathrin Bringmann and Ben Kane PDF

Trans. Amer. Math. Soc. 363 (2011), 2191-2209 Request permission

Abstract:

Andrews, Dyson, and Hickerson showed that 2 $q$-hypergeometric series, going back to Ramanujan, are related to real quadratic fields, which explains interesting properties of their Fourier coefficients. There is also an interesting relation of such series to automorphic forms. Here we construct more such examples arising from interesting combinatorial statistics.

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