Asymptotic normality and greatest common divisors

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 Fréchet distribution approximately. We also consider $r$-tuples instead of pairs, and moments other than the average.

References in corpus (2)

• On the probability distribution of the gcd and lcm of $r$-tuples of integers
• Pairwise Relative Primality of Positive Integers

Cited by in corpus (4)

• On the probability distribution of the gcd and lcm of $r$-tuples of integers
• Pairwise Relative Primality of Positive Integers
• Counting $r$-tuples of positive integers with $k$-wise relatively prime components
• Limit Theorems for Empirical Density of Greatest Common Divisors