The distribution of rationals in residue classes
Number Theory
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
Our purpose is to give an account of the -tuple problem on the increasing sequence of reduced fractions having denominators bounded by a certain size and belonging to a fixed real interval. We show that when the size grows to infinity, the proportion of the -tuples of consecutive denominators with components in certain apriori fixed arithmetic progressions with the same ratio approaches a limit, which is independent on the interval. The limit is given explicitly and it is completely described in a few particular instances.
Cite
@article{arxiv.math/0511356,
title = {The distribution of rationals in residue classes},
author = {Cristian Cobeli and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:math/0511356},
year = {2007}
}
Comments
19 pages