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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 rr-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}
}
R2 v1 2026-06-21T23:23:52.428Z