Vol. 9, No. 1, 2016

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On the distribution of the greatest common divisor of Gaussian integers

Tai-Danae Bradley, Yin Choi Cheng and Yan Fei Luo

Vol. 9 (2016), No. 1, 27–40
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.

Keywords
Gaussian integer, gcd, moment, Dedekind zeta function
Mathematical Subject Classification 2010
Primary: 11N37, 11A05, 11K65, 60E05