Limit Theorems for Empirical Density of Greatest Common Divisors
Probability
2016-10-07 v4 Number Theory
Abstract
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical density. We will also obtain a rate of convergence to the normal distribution for the central limit theorem. Some generalizations are provided.
Keywords
Cite
@article{arxiv.1310.7260,
title = {Limit Theorems for Empirical Density of Greatest Common Divisors},
author = {Behzad Mehrdad and Lingjiong Zhu},
journal= {arXiv preprint arXiv:1310.7260},
year = {2016}
}
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18 pages