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/Q is abelian and has degree at least four. As an application we also improve for such number fields on available results on counting pairs of coprime ideals each having norm at most x.
Counting ideals in abelian number fields
Alessandro Languasco;
2025
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/Q is abelian and has degree at least four. As an application we also improve for such number fields on available results on counting pairs of coprime ideals each having norm at most x.
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