标题： 论数域中互质分数的比例 显示英文标题

标题： On the Proportion of Coprime Fractions in Number Fields

摘要： 在本文中，我们确定了数域中既约分数中互质分数的渐近密度。 当按分母的范数排序时，我们一旦“出现”就将分数计入，不再之后计入。 然后可以使用关于Hecke$L$函数的已知事实来计算既约分数集合中互质分数的自然密度。 此外，我们还将其与模群和Heegner点联系起来。 显示英文摘要

摘要： 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.