# Journal of the Ramanujan Mathematical Society

Volume 34, Issue 4, December 2019  pp. 417–426.

New Infinite Families of Congruences Modulo 3, 5 and 7 for Overpartition Function

Authors:  Jubaraj Chetry and Nipen Saikia
Author institution:Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791 112, Arunachal Pradesh, India

Summary:  Let p (n) denote the number of overpartitions of a non-negative integer n. In this paper, we prove two new infinite families of congruences modulo 3 for p (n) by using Ramanujan's theta-function identities. Particularly, we prove that, for any integer α ≥ 0, p (9 α +1(24n+23)) ≡ 0 (mod 3) and p (9 α +1(24n+22)+1) ≡ 0 (mod 3). Furthermore, we prove some new congruences modulo 5 and 7 for p (n). For example, we prove that p (5n+k+3) ≡ 0 (mod 5), where k = 3n2 ± n.