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arXiv · 2303.11864

Asymptotic expansions for partitions generated by infinite products

Walter Bridges·Benjamin Brindle·Kathrin Bringmann·Johann Franke
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Abstract

Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in $\mathcal{L}\subset\mathbb{N}$ ($\gcd(\mathcal{L})=1$) and good analytic properties of the corresponding zeta function, generalizing work of Meinardus. In this paper, we extend their work to prove asymptotic formulas if $\mathcal{L}$ is a multiset of integers and the zeta function has multiple poles. In particular, our results imply an asymptotic formula for the number of irreducible representations of degree $n$ of $\mathfrak{so}{(5)}$. We also study the Witten zeta function $\zeta_{\mathfrak{so}{(5)}}$, which is of independent interest.

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Walter Bridges, Benjamin Brindle, Kathrin Bringmann, Johann Franke. 2023-03-21. Asymptotic expansions for partitions generated by infinite products. https://arxiv.org/abs/2303.11864

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