Some new infinite families of congruences modulo 3 for overpartitions into odd parts

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

Abstrakty

EN

Let $p̅_{o}(n)$ denote the number of overpartitions of n in which only odd parts are used. Some congruences modulo 3 and powers of 2 for the function $p̅_{o}(n)$ have been derived by Hirschhorn and Sellers, and Lovejoy and Osburn. In this paper, employing 2-dissections of certain quotients of theta functions due to Ramanujan, we prove some new infinite families of Ramanujan-type congruences for $p̅_{o}(n)$ modulo 3. For example, we prove that for n, α ≥ 0,
$p̅_{o}(4^{α}(24n+17)) ≡ p̅_{o}(4^{α}(24n+23)) ≡ 0 (mod 3)$.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 142
• Numer: 2
• Strony: 255-266

Daty

wydano

2016

Twórcy

autor

Ernest X. W. Xia

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

Identyfikatory

DOI

10.4064/cm142-2-6