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arXiv · 2607.08460

Rademacher-type formula and higher order Tur\'{a}n inequalities for $\ell$-regular overpartitions

Priyanka Dey·Ajit Singh·Gurinder Singh
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Abstract

For $\ell\geq 2$, let $\overline{A}_\ell(n)$ count the number of overpartitions of $n$ with no parts divisible by $\ell$. In this article, we employ the circle method to derive a Rademacher-type formula for $\overline{A}_\ell(n)$, when $\ell$ is a squarefree odd integer. As an application, we derive higher order Tu\'{r}an inequalities for the $\ell$-regular overpartition function using a result of Griffin, Ono, Rolen, and Zagier.

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Priyanka Dey, Ajit Singh, Gurinder Singh. 2026-07-09. Rademacher-type formula and higher order Tur\'{a}n inequalities for $\ell$-regular overpartitions. https://arxiv.org/abs/2607.08460

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