Modularity of moments of reciprocal sums for partitions into distinct parts

2025/04/10 by Bringmann, Kathrin, Kim, Byungchan, Kim, Eunmi · 1 citation
#11F20 #11P82 #11P83 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.07644

Abstract

In this paper, we determine modularity properties of the generating function of 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) is related to Maass Eisenstein series and sesquiharmonic Maass forms.

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• Applications of Faà di Bruno's formula to partition traces

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