Ranks of overpartitions: Asymptotics and inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Ciolan, Alexandru¹ 

[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

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

DOI  :  10.1016/j.jmaa.2019.123444

来源: Elsevier

【 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.

【 授权许可】

Free