New infinite families of Ramanujan-type congruences modulo 9 for overpartition pairs

• Autorzy: Ernest X. W. Xia
• Języki publikacji: EN

Abstrakty

EN

Let $\overline{pp}(n)$ denote the number of overpartition pairs of n. Bringmann and Lovejoy (2008) proved that for n ≥ 0, $\overline{pp}(3n+2) ≡ 0 (mod 3)$. They also proved that there are infinitely many Ramanujan-type congruences modulo every power of odd primes for $\overline{pp}(n)$. Recently, Chen and Lin (2012) established some Ramanujan-type identities and explicit congruences for $\overline{pp}(n)$. Furthermore, they also constructed infinite families of congruences for $\overline{pp}(n)$ modulo 3 and 5, and two congruence relations modulo 9. In this paper, we prove several new infinite families of congruences modulo 9 for $\overline{pp}(n)$. For example, we find that for all integers k,n ≥ 0, $\overline{pp}(2^{6k}(48n+20)) ≡ \overline{pp}(2^{6k}(384n+32)) ≡ \overline{pp}(2^{3k}(48n+36)) ≡ 0 (mod 9)$.

Kategorie tematyczne

• 11P83: Partitions; congruences and congruential restrictions
• 05A17: Partitions of integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 140
• Numer: 1
• Strony: 91-105

Daty

wydano

2015

Twórcy

autor

Ernest X. W. Xia

• Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R. China

Identyfikatory

DOI

10.4064/cm140-1-8