Institute of Mathematical Statistics Lecture Notes - Monograph Series

On the distribution of the greatest common divisor

Persi Diaconis and 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.

Chapter information

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

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285379

Digital Object Identifier
doi:10.1214/lnms/1196285379

Mathematical Reviews number (MathSciNet)
MR2126886

Subjects
Primary: 11N37: Asymptotic results on arithmetic functions 11A25: Arithmetic functions; related numbers; inversion formulas 60E05: Distributions: general theory

Keywords
Euler constant gcd inversion lcm moment random zeta function

Rights
Copyright © 2004, Institute of Mathematical Statistics

Citation

Diaconis, Persi; Erdös, Paul. On the distribution of the greatest common divisor. A Festschrift for Herman Rubin, 56--61, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196285379. https://projecteuclid.org/euclid.lnms/1196285379


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