Multiplicative $q$-hypergeometric series arising from real quadratic fields

TL;DR

This paper constructs new multiplicative q-hypergeometric series linked to real quadratic fields, expanding understanding of their properties and connections to automorphic forms through combinatorial statistics.

Contribution

It introduces novel examples of q-hypergeometric series associated with real quadratic fields derived from combinatorial statistics, extending prior work by Andrews, Dyson, and Hickerson.

Findings

New q-hypergeometric series linked to real quadratic fields.

Connections established between these series and automorphic forms.

Enhanced understanding of Fourier coefficients in related series.

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.