Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions

Open Mathematics

Liu Eric H.¹  Du Wenjing² 

[1] School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, 201620, P. R. China;Wenbo College, East China University of Political Science and Law, Shanghai, 201620, P. R. China;

关键词: congruence;    singular overpartition;    theta function;    11p83;    05a17;   

DOI  :  10.1515/math-2019-0026

来源: DOAJ

【 摘 要 】

Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined. A number of congruences modulo 3, 9 and congruences modulo powers of 2 for Ck,i(n) were discovered by Ahmed and Baruah, Andrews, Chen, Hirschhorn and Sellers, Naika and Gireesh, Shen and Yao for some pairs (k, i). In this paper, we prove some congruences modulo powers of 2 for C48, 6(n) and C48, 18(n).

【 授权许可】

Unknown