An improvement on the parity of Schur's partition function

被引：0

作者：

Lu, Yiwen ^{[1
]}

Wei, Tao ^{[1
]}

Guo, Xuejun ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 528卷 / 02期

关键词：

Schur's partition function; Parity; REPRESENTATIONS; NUMBER;

D O I：

10.1016/j.jmaa.2023.127530

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We improve S.-C. Chen's result on the parity of Schur's partition function. Let A(n) be the number of Schur's partitions of n, i.e., the number of partitions of n into distinct parts congruent to 1, 2 (mod 3). S.-C. Chen [3] shows x (log x) n < x : A(2n + 1) is odd} & DLANGBRAC; x (log x) x (log x) 11 12 47 48 ⠃ t1{0 < . In this paper, we improve Chen's result to 1 2 ⠃ t1{0 < n < x : A(2n + 1) is odd} K (log xx) 1 . 2 & COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：12

共 13 条

[1]

Ahlgren S., 2001, NOTICES AM MATH SOC, V48, P978

[2]

Andrews G.E., 1971, COMPUTERS NUMBER THE, P377

[3] Parity of Schur's partition function [J].

Chen, Shi-Chao .

COMPTES RENDUS MATHEMATIQUE, 2019, 357 (05) :418-423

[4]

Cox DA., 2013, . Pure and Applied Mathematics, V2

[5] ROOTS OF UNITY AND NULLITY MODULO n [J].

Finch, Steven ;

Martin, Greg ;

Sebah, Pascal .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (08) :2729-2743

[6] The number of representations function for binary quadratic forms [J].

Hall, NA .

AMERICAN JOURNAL OF MATHEMATICS, 1940, 62 :589-598

[7]

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

[8]

Kolberg O., 1959, Math. Scand., V7, P377

[9] ON DISTRIBUTION OF PARITY IN PARTITION FUNCTION [J].

PARKIN, TR ;

SHANKS, D .

MATHEMATICS OF COMPUTATION, 1967, 21 (99) :466-&

[10]

Rademacher H, 1937, P LOND MATH SOC, V43, P241

← 1 2 →