The probability of relatively prime polynomials in \(\mathbb Z_{p^k}[x]\)
type: Item
instance of: scholarly article
title: The probability of relatively prime polynomials in \(\mathbb Z_{p^k}[x]\)
zbMATH Open document ID: 1219.11050
author: Thomas R. Hagedorn
author: Jeffrey Hatley
published in: Involve
publication date: 2010-09-09T00:00:00Z
full work available at URL: p08.xhtml
review text: Let \(P_R(m,n)\) be the probability that two monic polynomials of degrees \(m\) and \(n\), randomly chosen in \(R[x]\), are relatively prime. For the finite field \(R={\mathbb F}_q\), we have \(P_R(m,n)=1-q^{-1}\) for all \(m,n\geq1\). In this paper, the authors study the probability for the ring \(R={\mathbb Z}_q\) of integers modulo \(q\) and give an explicit formula for \(P_R(m,2)\) where \(q\) is an odd prime power.
reviewed by: Astrid Reifegerste
Mathematics Subject Classification ID: 11C20
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 5781534
zbMATH Keywords: polynomials over integers modulo q
zbMATH Keywords: relative prime polynomials
MaRDI profile type: Publication
OpenAlex ID: W2133151326
DOI: 10.2140/INVOLVE.2010.3.223
description: scientific article; zbMATH DE number 5781534