Limiting joint distribution of greatest common divisors in random hypercubes

Abstract

The limiting distribution of the greatest common divisor (gcd) of a $D$-tuple of random natural numbers is known. We generalise this by determining an infinite product representation for the joint distribution of gcd-s in a $D$-dimensional hypercube of fixed but arbitrary side length around a $D$-tuple of random natural numbers. This allows for calculation of any statistic of the gcd-s within this hypercube, such as the number of coprime $D$-tuples.

Publication
preprint
István Kolossváry
István Kolossváry
Research Fellow