On the distribution of the greatest common divisor

Diaconis, Persi, Stanford University; Erdös, Paul, Stanford University

doi:10.1214/lnms/1196285379

VOL. 45 | 2004 On the distribution of the greatest common divisor

Persi Diaconis, Paul Erdös

Editor(s) Anirban DasGupta

IMS Lecture Notes Monogr. Ser., 2004: 56-61 (2004) DOI: 10.1214/lnms/1196285379

Abstract

For two integers chosen independently at random from {1, 2, . . . , x}, we give expansions for the distribution and the moments of their greatest common divisor and the least common multiple, with explicit error rates. The expansion involves Riemann’s zeta function. Application to a statistical question is briefly discussed.