title: 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 normxor less asxgoes 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 Erdös.
authors.affiliation: B.S. P rogram in M athematics , T he C ity C ollege of N ew Y ork , C onvent A ve . at 138 th S t ., NY 10031.
authors.forename: Tai-Danae
authors.initials: TD
authors.lastname: Bradley
authors.affiliation: B.S. P rogram in M athematics , T he C ity C ollege of N ew Y ork , C onvent A ve . at 138 th S t ., NY 10031.
authors.forename: Yin Choi
authors.initials: YC
authors.lastname: Cheng
authors.affiliation: B.S. P rogram in M athematics , T he C ity C ollege of N ew Y ork , C onvent A ve . at 138 th S t ., NY 10031.
authors.forename: Yan Fei
authors.initials: YF
authors.lastname: Luo
keywords: Dedekind zeta function; Gaussian integer; gcd; moment