%0 Journal Article
%T Limit Theorems for Empirical Density of Greatest Common Divisors
%A Behzad Mehrdad
%A Lingjiong Zhu
%J Mathematics
%D 2013
%I arXiv
%X 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 sharp rate of convergence to the normal distribution for the central limit theorem. Some generalizations are provided.
%U http://arxiv.org/abs/1310.7260v3