LAUSR

Andrews, Dyson and Hickerson proved many interesting properties of coefficients for a Ramanujan’s q-hypergeometric series by relating it to real quadratic field ℚ(6) and using the arithmetic of ℚ(6) to solve a conjecture of Andrews on the distributions of its Fourier coefficients. Motivated by Andrews’s conjecture, we discuss an interesting q-hypergeometric series which comes from a Lerch sum and rank and crank moments for partitions and overpartitions. We give Andrews-like conjectures for its coefficients. We obtain partial results on the distributions of small values of its coefficients toward these conjectures.