Limit Theorems for Empirical Density of Greatest Common Divisors

作者:Mehrdad Behzad*; Zhu Lingjiong
来源:Mathematical Proceedings of the Cambridge Philosophical Society, 2016, 161(3): 517-533.
DOI:10.1017/S0305004116000426

摘要

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.

  • 出版日期2016-11