On the distribution of the greatest common divisor
Persi Diaconis, Paul Erdös
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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.
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Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196285379
Mathematical Reviews (MathSciNet):
MR2126886
Digital Object Identifier: doi:10.1214/lnms/1196285379
Institute of Mathematical Statistics Lecture Notes - Monograph Series