On the Proportion of Coprime Fractions in Number Fields
Number Theory
2024-03-28 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 -functions. Furthermore, we draw some connections to the modular group and Heegner points.
Keywords
Cite
@article{arxiv.2311.01346,
title = {On the Proportion of Coprime Fractions in Number Fields},
author = {Walter Bridges and Johann Franke and Johann Christian Stumpenhusen},
journal= {arXiv preprint arXiv:2311.01346},
year = {2024}
}
Comments
12 pages, 1 figure, 1 table