On the asymptotic behavior of unimodal rank generating functions

被引：6

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：

欧洲研究理事会; 新加坡国家研究基金会;

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.

引用

页码：627 / 645

页数：19

共 34 条

[21] Higher rank partial and false theta functions and representation theory [J].

Creutzig, Thomas ;

Milas, Antun .

ADVANCES IN MATHEMATICS, 2017, 314 :203-227

[22] Some new asymptotic expansions of certain partial theta functions [J].

Renrong Mao .

The Ramanujan Journal, 2014, 34 :443-448

[23] Some new asymptotic expansions of certain partial theta functions [J].

Mao, Renrong .

RAMANUJAN JOURNAL, 2014, 34 (03) :443-448

[24] The Averaging Method and the Asymptotic Behavior of Solutions to Differential Inclusions [J].

Klimov, V. S. ;

Ukhalov, A. Yu. .

RUSSIAN MATHEMATICS, 2009, 53 (08) :20-28

[25] The averaging method and the asymptotic behavior of solutions to differential inclusions [J].

V. S. Klimov ;

A. Yu. Ukhalov .

Russian Mathematics, 2009, 53 (8) :20-28

[26] Asymptotic formulas related to the M2-rank of partitions without repeated odd parts [J].

Jennings-Shaffer, Chris ;

Reihill, Dillon .

RAMANUJAN JOURNAL, 2020, 52 (01) :175-242

[27] Asymptotic expansions for double Shintani zeta-functions of several variables [J].

Katsurada, Masanori .

DIOPHANTINE ANALYSIS AND RELATED FIELDS 2011 (DARF 2011), 2011, 1385 :58-72

[28] Projection-Based Model Reduction Using Asymptotic Basis Functions [J].

Cassel, Kevin W. .

COMPUTATIONAL SCIENCE - ICCS 2019, PT IV, 2019, 11539 :465-478

[29] Complete asymptotic expansions associated with Epstein zeta-functions II [J].

Katsurada, Masanori .

RAMANUJAN JOURNAL, 2015, 36 (03) :403-437

[30] APPROXIMATION OF THE UNSTATIONARY MAXWELL EQUATIONS IN AN UNBOUNDED DOMAIN ASYMPTOTIC-BEHAVIOR [J].

HELLUY, P ;

MAZET, P ;

KLOTZ, P .

RECHERCHE AEROSPATIALE, 1994, (05) :365-377

← 1 2 3 4 →