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Limit Theorems for Empirical Density of Greatest Common Divisors
Published online by Cambridge University Press: 23 May 2016
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. 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.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 3 , November 2016 , pp. 517 - 533
- Copyright
- Copyright © Cambridge Philosophical Society 2016
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