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arXiv · 2603.22775

On the series expansion of k-free Dirichlet series and its analytical continuation

Artur Kawalec
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Abstract

In this article, we develop a k-free zeta Dirichlet series into a Laurent series with a simple pole, and prove a Stieltjes like formula for the expansion coefficients of the regular part. We also investigate another analytical continuation of these series and develop a formula for $\zeta(\tfrac{1}{k})$ for positive integer $k\geq 2$ in terms of the k-free indicator function.

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Artur Kawalec. 2026-03-24. On the series expansion of k-free Dirichlet series and its analytical continuation. https://arxiv.org/abs/2603.22775

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