Certain eta-quotients and $$\ell $$-regular overpartitions
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DOI: 10.1007/s11139-020-00322-6
Abstract: Let $${\overline{A}}_{\ell }(n)$$ be the number of overpartitions of n into parts not divisible by $$\ell $$ . In this paper, we prove that $${\overline{A}}_{\ell }(n)$$ is almost always divisible by $$p_i^j$$ if $$p_i^{2a_i}\ge \ell… read more here.
Keywords: certain eta; quotients ell; eta quotients; regular overpartitions ... See more keywords
Parity of the coefficients of certain eta-quotients
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DOI: 10.1016/j.jnt.2021.06.034
Abstract: We investigate the parity of the coefficients of certain eta-quotients, extensively examining the case of $m$-regular partitions. Our theorems concern the density of their odd values, in particular establishing lacunarity modulo 2 for specified coefficients;… read more here.
Keywords: certain eta; parity coefficients; eta quotients; coefficients certain ... See more keywords