%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