Asymptotic normality and greatest common divisors

José L. Fernández, Pablo Fernández

Published 2013-02-10, updated 2013-05-08Version 2

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 $r$-tuples instead of pairs, and moments other than the average.