On the distribution of the greatest common divisor
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Institute of Mathematical Statistics Lecture Notes - Monograph Series

On the distribution of the greatest common divisor

Persi Diaconis, Paul Erdös

Source: Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 56-61.

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.

Primary Subjects: 11N37, 11A25, 60E05
Keywords: Euler constant; gcd; inversion; lcm; moment; random; zeta function

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196285379
Mathematical Reviews (MathSciNet): MR2126886

Digital Object Identifier: doi:10.1214/lnms/1196285379

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2009 © Institute of Mathematical Statistics

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Institute of Mathematical Statistics Lecture Notes - Monograph Series