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2016 On the distribution of the greatest common divisor of Gaussian integers
Tai-Danae Bradley, Yin Choi Cheng, Yan Fei Luo
Involve 9(1): 27-40 (2016). DOI: 10.2140/involve.2016.9.27

Abstract

For a pair of random Gaussian integers chosen uniformly and independently from the set of Gaussian integers of norm x or less as x goes to infinity, we find asymptotics for the average norm of their greatest common divisor, with explicit error terms. We also present results for higher moments along with computational data which support the results for the second, third, fourth, and fifth moments. The analogous question for integers is studied by Diaconis and Erdős.

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Tai-Danae Bradley. Yin Choi Cheng. Yan Fei Luo. "On the distribution of the greatest common divisor of Gaussian integers." Involve 9 (1) 27 - 40, 2016. https://doi.org/10.2140/involve.2016.9.27

Information

Received: 27 March 2013; Revised: 9 January 2015; Accepted: 28 January 2015; Published: 2016
First available in Project Euclid: 22 November 2017

zbMATH: 1330.11058
MathSciNet: MR3438443
Digital Object Identifier: 10.2140/involve.2016.9.27

Subjects:
Primary: 11A05 , 11K65 , 11N37 , 60E05

Keywords: Dedekind zeta function , Gaussian integer , gcd , Moment

Rights: Copyright © 2016 Mathematical Sciences Publishers

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