Congruences modulo 8 for $$(2,\, k)$$ -regular overpartitions for odd $$k > 1$$

Arabian Journal of Mathematics, Dec 2017

In this paper, we study various arithmetic properties of the function $$\overline{p}_{2,\,\, k}(n)$$, which denotes the number of $$(2,\,\, k)$$-regular overpartitions of n with odd $$k > 1$$. We prove several infinite families of congruences modulo 8 for $$\overline{p}_{2,\,\, k}(n)$$. For example, we find that for all non-negative integers $$\beta , n$$ and $$k\equiv 1\pmod {8}$$, $$\overline{p}_{2,\,\, k}(2^{1+\beta }(16n+14))\equiv ~0\pmod {8}$$.

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Chandrashekar Adiga, M. S. Mahadeva Naika, D. Ranganatha, C. Shivashankar. Congruences modulo 8 for $$(2,\, k)$$ -regular overpartitions for odd $$k > 1$$, Arabian Journal of Mathematics, 2017, 1-15, DOI: 10.1007/s40065-017-0195-z