On the asymptotic behavior of unimodal rank generating functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Bringmann, Kathrin¹  Kim, Byungchan² 

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

[2] Seoul Natl Univ Sci & Technol, Sch Liberal Arts, Seoul 01811, South Korea

关键词: Unimodal sequences;    Unimodal ranks;    Circle Method;    Partial theta functions;    Asymptotic methods;   

DOI  :  10.1016/j.jmaa.2015.10.057

来源: Elsevier

【 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.

【 授权许可】

Free