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}
}
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. 

From This Paper

Topics from this paper.
1 Citations
13 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 13 references

Asymptotic normality and greatest common divisors

  • J. L. Fernández, P. Fernández
  • 2013
Highly Influential
6 Excerpts

Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York, NY-10012 United States of America E-mail address: mehrdad@cims.nyu.edu, ling@cims.nyu.edu

  • S.R.S. Varadhan
  • Large Deviations and Applications, SIAM…
  • 1984
Highly Influential
3 Excerpts

On the probability distribution of gcd and lcm of r-tuples of integers

  • J. L. Fernández, P. Fernández
  • 2013
1 Excerpt

An Introduction to the Theory of Numbers, 6th Edition

  • G. H. Hardy, E. M. Wright
  • 2008

Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics

  • G. Tenenbaum
  • 1995
2 Excerpts

A normal approximation for the number of local maxima of a random function on a graph

  • P. Baldi
  • Papers in Honor of Samuel Karlin
  • 1989

A normal approximation for the number of local maxima of a random function on a graph. In Probability, Statistics, and Mathematics

  • P. Baldi, Y. Rinott, C. Stein
  • Papers in Honor of Samuel Karlin (T
  • 1989
2 Excerpts

Probabilistic Number Theory, Volume I and II, Springer-Verlag

  • Elliott, A P.D.T.
  • New York,
  • 1980
2 Excerpts

On the distribution of the greatest common divisor

  • P. Diaconis, P. Erdős
  • Technical Report No. 12. Stanford University,
  • 1977
3 Excerpts

Similar Papers

Loading similar papers…