New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions

作者：Yao Olivia X M^*; Xia Ernest X W

来源：Journal of Number Theory, 2013, 133(6): 1932-1949.

DOI：10.1016/j.jnt.2012.11.002

• Overpartition
• Congruence
• 2-Dissection

Let (p) over bar (n) denote the number of overpartitions of n. In recent works, Fortin, Jacob and Mathieu, and Hirschhorn and Sellers established some congruences modulo powers of 2 for (p) over bar (n). Much less is known for powers of 3. In this paper, employing elementary generating function dissection techniques, we prove that for all nonnegative integers n,
(p) over bar (24n + 19) equivalent to 0 (mod 27)
and
(p) over bar (92n + 12) equivalent to 0 (mod 9).
Furthermore, we also derive some new congruences modulo powers of 2 for (p) over bar (n).

• 出版日期2013-6
• 单位江苏大学