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arXiv · 1712.03015

On the logarithmic probability that a random integral ideal is $\mathscr A$-free

Christian Huck
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Abstract

This extends a theorem of Davenport and Erdös on sequences of rational integers to sequences of integral ideals in arbitrary number fields $K$. More precisely, we introduce a logarithmic density for sets of integral ideals in $K$ and provide a formula for the logarithmic density of the set of so-called $\mathscr A$-free ideals, i.e. integral ideals that are not multiples of any ideal from a fixed set $\mathscr A$.

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Christian Huck. 2017-12-08. On the logarithmic probability that a random integral ideal is $\mathscr A$-free. https://doi.org/10.1007/978-3-319-74908-2_13

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