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arXiv · 2301.02377

On square-free numbers generated from given sets of primes II

Gábor Román
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Abstract

We progress with the investigation started in article \cite{Roman2022}, namely the analysis of the asymptotic behaviour of $Q_{\mathcal{P}}(x)$ for different sets $\mathcal{P}$, where $Q_{\mathcal{P}}(x)$ is the element count of the set containing those positive square-free integers, which are smaller than-, or equal to $x$, and which are only divisible by the elements of $\mathcal{P}$. We study how $Q_{\mathcal{P}}(x)$ behaves when we require that $\chi(p) = 1$ must hold for every $p \in \mathcal{P}$, where $\chi$ is a Dirichlet character.

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Gábor Román. 2023-01-06. On square-free numbers generated from given sets of primes II. https://arxiv.org/abs/2301.02377

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