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
Rights: Copyright © 2004, Institute of Mathematical Statistics
