On the degree of the GCD of random polynomials over a finite field
type: Item
instance of: scholarly article
title: On the degree of the GCD of random polynomials over a finite field
zbMATH Open document ID: 1477.11004
DOI: 10.1155/2021/3619347
author: Kui Liu
author: Meijie Lu
published in: Journal of Mathematics
publication date: 2021-11-25T00:00:00Z
review text: Summary: In this paper, we focus on the degree of the greatest common divisor (gcd) of random polynomials over \(\mathbb{F}_q\). Here, \(\mathbb{F}_q\) is the finite field with \(q\) elements. Firstly, we compute the probability distribution of the degree of the gcd of random and monic polynomials with fixed degree over \(\mathbb{F}_q\). Then, we consider the waiting time of the sequence of the degree of gcd functions. We compute its probability distribution, expectation, and variance. Finally, by considering the degree of a certain type gcd, we investigate the probability distribution of the number of rational (i.e., in \(\mathbb{F}_q\)) roots (counted with multiplicity) of random and monic polynomials with fixed degree over \(\mathbb{F}_q\).
Mathematics Subject Classification ID: 11A05
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 7433534
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/3619347
OpenAlex ID: W3199287536
cites work: Arithmetical Functions of a Greatest Common Divisor. I
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cites work: Roots of random polynomials over a finite field
description: scientific article; zbMATH DE number 7433534