Degree distribution of the greatest common divisor of polynomials over 𝔽q

Abstract

AbstractWe study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field 𝔽q. We provide estimates for several parameters like number of distinct common irreducible factors, number of irreducible factors counting repetitions, and total degree of the gcd of two or more polynomials. We show that the limiting distribution of a random variable counting the total degree of the gcd is geometric and that the distributions of random variables counting the number of common factors (with and without repetitions) are very close to Poisson distributions when q is large. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006