## Involve: A Journal of Mathematics

• Involve
• Volume 9, Number 1 (2016), 27-40.

### On the distribution of the greatest common divisor of Gaussian integers

#### 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.

#### Article information

Source
Involve, Volume 9, Number 1 (2016), 27-40.

Dates
Revised: 9 January 2015
Accepted: 28 January 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511370969

Digital Object Identifier
doi:10.2140/involve.2016.9.27

Mathematical Reviews number (MathSciNet)
MR3438443

Zentralblatt MATH identifier
1330.11058

#### Citation

Bradley, Tai-Danae; Cheng, Yin Choi; Luo, Yan Fei. On the distribution of the greatest common divisor of Gaussian integers. Involve 9 (2016), no. 1, 27--40. doi:10.2140/involve.2016.9.27. https://projecteuclid.org/euclid.involve/1511370969

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