Degree distribution of the greatest common divisor of polynomials over double-struck F signq
We study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field double-struck F signq. 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.
|Keywords||Degree distributions, Greatest common divisor of polynomials, Probability generating functions|
|Journal||Random Structures and Algorithms|
Gao, Z, & Panario, D. (2006). Degree distribution of the greatest common divisor of polynomials over double-struck F signq. Random Structures and Algorithms, 29(1), 26–37. doi:10.1002/rsa.20093