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arXiv · 2504.09469

Counting ideals in abelian number fields

Alessandro Languasco·Rashi Lunia·Pieter Moree
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Abstract

Already Dedekind and Weber considered the problem of counting integral ideals of norm at most $x$ in a given number field $K$. Here we improve on the existing results in case $K/\mathbb Q$ is abelian and has degree at least four. For these fields, we obtain as a consequence an improvement of the available results on counting pairs of coprime ideals each having norm at most $x$.

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Alessandro Languasco, Rashi Lunia, Pieter Moree. 2025-04-13. Counting ideals in abelian number fields. https://doi.org/10.1016/j.jnt.2025.10.012

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