On weighted overpartitions related to some q-series in Ramanujan's lost notebook

摘要

Motivated by certain q-series of Ramanujan, we examine two overpartition difference functions. We give both combinatorial and asymptotic formulas for the differences and show that they are always positive. We also briefly discuss similar differences for some other types of partitions. Our main tools are elementary q-series transformations and Ingham's Tauberian theorem.