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. 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 .
Counting ideals in abelian number fields
Alessandro Languasco;
2026
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. 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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