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

Ernest X. W. Xia. "Some new infinite families of congruences modulo 3 for overpartitions into odd parts." Colloquium Mathematicae 142.2 (2016): 255-266. <http://eudml.org/doc/284139>.

@article{ErnestX2016,
abstract = {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, $p̅_\{o\}(4^\{α\}(24n+17)) ≡ p̅_\{o\}(4^\{α\}(24n+23)) ≡ 0 (mod 3)$.},
author = {Ernest X. W. Xia},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {255-266},
title = {Some new infinite families of congruences modulo 3 for overpartitions into odd parts},
url = {http://eudml.org/doc/284139},
volume = {142},
year = {2016},
}

TY - JOUR
AU - Ernest X. W. Xia
TI - Some new infinite families of congruences modulo 3 for overpartitions into odd parts
JO - Colloquium Mathematicae
PY - 2016
VL - 142
IS - 2
SP - 255
EP - 266
AB - 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, $p̅_{o}(4^{α}(24n+17)) ≡ p̅_{o}(4^{α}(24n+23)) ≡ 0 (mod 3)$.
LA - eng
UR - http://eudml.org/doc/284139
ER -