Numerators of differences of nonconsecutive Farey fractions
Numerators of differences of nonconsecutive Farey fractions
复制标题
非连续法雷分数差的分子
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Haynes
中科院分区：
文献类型：
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作者：
A. Haynes
一个基本但有用的事实是，两个连续的法里分数的差的分子等于一。对于连续分数的三元组，差异的分子是很好理解的，并应用于几个有趣的问题。本文研究了距离较远的分数差的分子。我们建立这样的差异之间的代数身份，然后让我们计算它们的平均值，通过使用属性的措施保持变换的Farey三角形。
An elementary but useful fact is that the numerator of the difference of two consecutive Farey fractions is equal to one. For triples of consecutive fractions the numerators of the differences are well understood and have applications to several interesting problems. In this paper we investigate numerators of differences of fractions which are farther apart. We establish algebraic identities between such differences which then allow us to calculate their average values by using properties of a measure preserving transformation of the Farey triangle.