References & Citations
Mathematics > Number Theory
Title: On the Proportion of Coprime Fractions in Number Fields
(Submitted on 2 Nov 2023 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fraction as soon as it ``appears'' for the first time and no later. The natural density of coprime fractions in the set of reduced fractions may then be computed using well-known facts about Hecke $L$-functions. Furthermore, we draw some connections to the modular group and Heegner points.
Submission history
From: Johann Stumpenhusen [view email][v1] Thu, 2 Nov 2023 15:56:44 GMT (41kb,D)
[v2] Wed, 27 Mar 2024 07:21:57 GMT (41kb,D)
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