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arXiv · 1409.6527

On Mertens-Cesàro Theorem for Number Fields

Andrea Ferraguti·Giacomo Micheli
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Abstract

Let $K$ be a number field with ring of integers $\mathcal O$. After introducing a suitable notion of density for subsets of $\mathcal O$, generalizing that of natural density for subsets of $\mathbb Z$, we show that the density of the set of coprime $m$-tuples of algebraic integers is ${1/ζ_K(m)}$, where $ζ_K$ is the Dedekind zeta function of $K$.

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Andrea Ferraguti, Giacomo Micheli. 2015-09-03. On Mertens-Cesàro Theorem for Number Fields. https://doi.org/10.1017/s0004972715001288

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