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arXiv · 2609.14538

Asymptotic Formula for Biregular Overpartitions

Jayanta Barman
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Abstract

Let $\bar{p}_{s,t}(N)$ be the number of overpartitions of $N$ into parts that are not divisible by $s$ or $t$. In this paper, we obtain asymptotic formulas for $\bar{p}_{s,t}(N)$ for relatively prime integers $s>t\ge 10$ via the saddle-point method. Our results cover different ranges of the parameters $s$ and $t$ relative to $N$. As an application, we show that $\bar{p}_{s,t}(N)$ satisfies higher-order Turán inequalities for all sufficiently large $N$ by using a result of Griffin, Ono, Rolen, and Zagier.

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Jayanta Barman. 2026-09-13. Asymptotic Formula for Biregular Overpartitions. https://arxiv.org/abs/2609.14538

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