On the asymptotic behavior of unimodal rank generating functions

被引：5
作者：
Bringmann, Kathrin [1 ]
Kim, Byungchan [2 ]
机构：
[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany
[2] Seoul Natl Univ Sci & Technol, Sch Liberal Arts, Seoul 01811, South Korea
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 435卷 / 01期
基金：
新加坡国家研究基金会; 欧洲研究理事会;
关键词：
Unimodal sequences; Unimodal ranks; Circle Method; Partial theta functions; Asymptotic methods; RAMANUJAN; STACKS;
D O I：
10.1016/j.jmaa.2015.10.057
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we use Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions. (C) 2015 Elsevier Inc. All rights reserved.
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页码：627 / 645
页数：19
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