Involve: A Journal of Mathematics

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

On the distribution of the greatest common divisor of Gaussian integers

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

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N37: Asymptotic results on arithmetic functions 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors 11K65: Arithmetic functions [See also 11Nxx] 60E05: Distributions: general theory

Gaussian integer gcd moment Dedekind zeta function


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.

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