Ranks of overpartitions: Asymptotics and inequalities

In this paper we compute asymptotics for the coefficients of an infinite class of overpartition rank generating functions. Using these results, we show that (N) over bar (a, c, n), the number of overpartitions of n with rank congruent to a modulo c, is equidistributed with respect to 0 = 2, as n -> infinity and, in addition, we prove some inequalities between ranks of overpartitions conjectured by Ji, Zhang and Zhao (2018), and Wei and Zhang (2018) for n = 6 and n = 10. (C) 2019 Elsevier Inc. All rights reserved