Ramanujan-Type Partial Theta Identities and Rank Differences for Special Unimodal Sequences

被引：9

作者：

Kim, Byungchan ^{[1
,2
]}

Lovejoy, Jeremy ^{[3
]}

机构：

[1] Seoul Natl Univ Sci & Technol, Sch Liberal Arts, Seoul 139743, South Korea

[2] Seoul Natl Univ Sci & Technol, Inst Convergence Fundamental Studies, Seoul 139743, South Korea

[3] Univ Paris 07, LIAFA, CNRS, F-75205 Paris 13, France

来源：

ANNALS OF COMBINATORICS | 2015年 / 19卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

unimodal sequences; rank; partial theta functions; INEQUALITIES; PARTITIONS; CRANK;

D O I：

10.1007/s00026-015-0281-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider three types of unimodal sequences related to Ramanujan-type partial theta identities. In each case we compute generating functions related to the rank and use the partial theta identity to give formulas for certain rank differences.

引用

页码：705 / 733

页数：29

共 34 条

[1] Rank generating functions as weakly holomorphic modular forms
Ahlgren, Scott
Treneer, Stephanie
[J]. ACTA ARITHMETICA, 2008, 133 (03) : 267 - 279
[2] Andrews GE, 2001, NATO SCI SER II MATH, V30, P1
[3] Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
Andrews, George E.
[J]. INVENTIONES MATHEMATICAE, 2007, 169 (01) : 37 - 73
[4] Andrews George E., 2009, Ramanujan's lost notebook
[5] Atkin A. O. L., 1954, P LOND MATH SOC, V4, P84, DOI [10.1112/plms/s3-4.1.84, DOI 10.1112/PLMS/S3-4.1.84]
[6] Berndt BC., 2006, NUMBER THEORY SPIRIT
[7] Bringmann K, 2008, J AM MATH SOC, V21, P1085
[8] Asymptotic formulas for stacks and unimodal sequences
Bringmann, Kathrin
Mahlburg, Karl
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2014, 126 : 194 - 215
[9] Bringmann K, 2014, T AM MATH SOC, V366, P1073
[10] Bringmann K, 2010, MATH RES LETT, V17, P927

← 1 2 3 4 →