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