Limit Theorems for Empirical Density of Greatest Common Divisors

2016 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
AbstractThe 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. 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 generalisations are provided.
doi:10.1017/s0305004116000426 fatcat:h2idp2chqffzzondaekncxajwy