Asymptotic normality and greatest common divisors
Probability
2015-12-16 v2
Abstract
We report on some statistical regularity properties of greatest common divisors: for large random samples of integers, the number of coprime pairs and the average of the gcd's of those pairs are approximately normal, while the maximum of those gcd's (appropriately normalized) follows approximately a Fr\'echet distribution approximately. We also consider -tuples instead of pairs, and moments other than the average.
Keywords
Cite
@article{arxiv.1302.2357,
title = {Asymptotic normality and greatest common divisors},
author = {José L. Fernández and Pablo Fernández},
journal= {arXiv preprint arXiv:1302.2357},
year = {2015}
}