Modularity of moments of reciprocal sums for partitions into distinct parts

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发表日期：

2025年8月7日

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Kathrin Bringmann,
Byungchan Kim,
Eunmi Kim

摘要

In this paper, we determine modularity properties of the generating function of $s_k(n)$ $s_{k} (n)$ which sums k-th power of reciprocals of parts throughout all of the partitions of n into distinct parts. In particular, we show that the generating function for $s_k (n)$ $s_{k} (n)$ is related to Maass Eisenstein series and sesquiharmonic Maass forms.