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# Limit Theorems for Empirical Density of Greatest Common Divisors

@inproceedings{Mehrdad2013LimitTF, title={Limit Theorems for Empirical Density of Greatest Common Divisors}, author={Behzad Mehrdad and Lingjiong Zhu}, year={2013} }

- Published 2013

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.

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