Ranks of overpartitions: Asymptotics and inequalities

被引：9
作者：
Ciolan, Alexandru [1 ]
机构：
[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 480卷 / 02期
基金：
欧洲研究理事会;
关键词：
Asymptotics; Circle method; Dyson's rank; Inequalities; Kloosterman sums; Overpartitions; COEFFICIENTS;
D O I：
10.1016/j.jmaa.2019.123444
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页数：28
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