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arXiv · 2403.07600

Asymptotic $\psi$-densities of subsets of natural numbers

Janne Heittokangas·Zinelaabidine Latreuch
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Abstract

The sizes of subsets of the natural numbers are typically quantified in terms of asymptotic (linear) and logarithmic densities. These concepts have been generalized to weighted $w$-densities, where a specific weight function $w$ plays a key role. In this paper, a parallel theory of asymptotic $\psi$-densities is introduced, where the weight is expressed slightly differently in terms of differentiable functions $\psi$, which are either concave or convex and satisfy certain asymptotic properties. Alternative new proofs for known results on analytic and Abel densities are also given.

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Janne Heittokangas, Zinelaabidine Latreuch. 2024-03-12. Asymptotic $\psi$-densities of subsets of natural numbers. https://arxiv.org/abs/2403.07600

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