Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the numberâ€¦ (More)

We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank momentsâ€¦ (More)

We prove that of all two-dimensional lattices of covolume 1 the hexagonal lattice has asymptotically the fewest distances. An analogous result for dimensions 3 to 8 was proved in 1991 by Conway andâ€¦ (More)

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analoguesâ€¦ (More)

Abstract. We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations ofâ€¦ (More)

The rank of a partition is the largest part minus the number of parts. This statistic was introduced by Dyson [14], who observed empirically that it provided a combinatorial explanation forâ€¦ (More)

This is the third and final installment in our series of papers applying the method of Atkin and Swinnerton-Dyer to deduce formulas for rank differences. The study of rank differences was initiatedâ€¦ (More)

Abstract. In [1], the authors established a method of determining the structure of the 2-Sylow subgroup of the tame kernel K2(O) for certain quadratic number fields. Specifically, the 4-rank forâ€¦ (More)

In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the firstâ€¦ (More)

Mixed mock modular forms are functions which lie in the tensor space of mock modular forms and modular forms. As q-hypergeometric series, mixed mock modular forms appear to be much more common thanâ€¦ (More)