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Chetry, Jubaraj
- New Infinite Families of Congruences Modulo 3, 5 and 7 For Overpartition Function
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1 Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791 112, Arunachal Pradesh, IN
1 Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791 112, Arunachal Pradesh, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 34, No 4 (2019), Pagination: 417-426Abstract
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(9α+1(24n + 23)) ≡ 0 (mod 3) and ¯p(9α+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.
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