Roots of random polynomials over a finite field
type: Item
instance of: scholarly article
title: Roots of random polynomials over a finite field
zbMATH Open document ID: 1121.60055
author: V. K. Leont'ev
published in: Mathematical Notes
publication date: 2007-05-21T00:00:00Z
review text: This is an interesting work on the number of roots of polynomials with random coefficients. The paper generalizes the classical and well known results of \textit{M. Kac} [Bull. Am. Math. Soc. 49, 314--320 (1943; Zbl 0060.28602)] in which he obtained the first asymptotic value for the expected number of real zeros of an algebraic polynomial \(\sum_{j=0}^n a_j x^j\) with random coefficient \(a_j\). This paper instead considers the ring of polynomials over a finite field and studies the number of its roots lying in the finite field. It is shown that this number asymptotically tends to a Poisson distribution with parameter one. Although results are mainly for the normalized polynomials, more general cases are also discussed.
reviewed by: Kambiz Farahmand
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 5155527
zbMATH Keywords: random polynomials
zbMATH Keywords: real roots
zbMATH Keywords: finite field
zbMATH Keywords: Poisson distribution
MaRDI profile type: Publication
full work available at URL: s11006-006-0139-y
OpenAlex ID: W2361038446
cites work: Q4146667
cites work: Q3259971
cites work: Q3900071
cites work: Q3665103
DOI: 10.1007/S11006-006-0139-Y
description: scientific article; zbMATH DE number 5155527