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arXiv · 2202.07763

Combinatorial formulas for arithmetic density

Robert Schneider·Andrew V. Sills
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Abstract

Let $d_S$ denote the arithmetic density of a subset $S \subseteq \mathbb N$. We derive a power series in $q\in \mathbb C$, $|q|<1$, with co\"efficients related to integer partitions and integer compositions, that yields $1/d_S$ in the limit as $q\to 1$ radially.

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Robert Schneider, Andrew V. Sills. 2022-02-16. Combinatorial formulas for arithmetic density. https://arxiv.org/abs/2202.07763

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