INEQUALITIES AND UNIFORM ASYMPTOTIC FORMULAE FOR SPT-CRANK OF PARTITIONS

被引：0

作者：

Chen, Yuan ^{[1
]}

Zhou, Nian Hong ^{[1
]}

机构：

[1] Guangxi Normal Univ, Sch Math & Stat, Guilin, Guangxi, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2025年 / 111卷 / 01期

关键词：

integer partitions; spt-crank; uniform asymptotics;

D O I：

10.1017/S0004972724000455

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish some inequalities that arise from truncating Lerch sums and derive uniform asymptotic formulae for the spt-crank of ordinary partitions. The uniform asymptotic formulae improve upon a result of Mao ['Asymptotic formulas for spt-crank of partitions', J. Math. Anal. Appl. 460(1) (2018), 121-139].

引用

页码：56 / 67

页数：12

共 8 条

[1] Combinatorial interpretations of congruences for the spt-function [J].

Andrews, George E. ;

Garvan, Frank G. ;

Liang, Jie .

RAMANUJAN JOURNAL, 2012, 29 (1-3) :321-338

[2] The odd moments of ranks and cranks [J].

Andrews, George E. ;

Chan, Song Heng ;

Kim, Byungchan .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2013, 120 (01) :77-91

[3] The number of smallest parts in the partitions of n [J].

Andrews, George E. .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 624 :133-142

[4] The spt-crank for ordinary partitions [J].

Chen, William Y. C. ;

Ji, Kathy Q. ;

Zang, Wenston J. T. .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2016, 711 :231-249

[5]

Hardy GH, 1918, P LOND MATH SOC, V17, P75

[6] Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions [J].

Liu, Zhi-Guo ;

Zhou, Nian Hong .

RAMANUJAN JOURNAL, 2022, 57 (03) :1085-1123

[7] Asymptotic formulas for spt-crank of partitions [J].

Mao, Renrong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 460 (01) :121-139

[8] Congruence properties of partitions. [J].

Ramanujan, S .

MATHEMATISCHE ZEITSCHRIFT, 1921, 9 :147-153

← 1 →