Ranks of overpartitions: Asymptotics and inequalities

[摘要] 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 <= a < c, for any c >= 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.

[发布日期] 2019-12-15

[关键词] Asymptotics;Circle method;Dyson's rank;Inequalities;Kloosterman sums;Overpartitions