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arXiv:2102.01379 [math.CO]AbstractReferencesReviewsResources

Overpartitions and functions from multiplicative number theory

Mircea Merca

Published 2021-02-02Version 1

Let $\alpha$ and $\beta$ be two nonnegative integers such that $\beta < \alpha$. For an arbitrary sequence $\{a_n\}_{n\geqslant 1}$ of complex numbers, we consider the generalized Lambert series in order to investigate linear combinations of the form $\sum_{k\geqslant 1} S(\alpha k-\beta,n) a_k$, where $S(k,n)$ is the total number of non-overlined parts equal to $k$ in all the overpartitions of $n$. The general nature of the numbers $a_n$ allows us to provide connections between overpartitions and functions from multiplicative number theory.

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