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

## 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.

## Information

Published: 1 January 2004
First available in Project Euclid: 28 November 2007

zbMATH: 1268.11139
MathSciNet: MR2126886

Digital Object Identifier: 10.1214/lnms/1196285379

Subjects:
Primary: 11A25 , 11N37 , 60E05

Keywords: Euler constant , gcd , inversion , lcm , Moment , random , zeta function