On the number of polynomials of small house
type: Item
instance of: scholarly article
title: On the number of polynomials of small house
zbMATH Open document ID: 0947.11032
DOI: 10.1007/BF02469281
published in: Lithuanian Mathematical Journal
publication date: 2000-10-04T00:00:00Z
review text: Let \(\varepsilon \) be a positive number and \(d\) be a sufficiently large positive integer. The author proves that the number of monic integer polynomials of degree \(d\) with integer coefficients whose roots are of moduli \({}\leq d^{\varepsilon /d}\) is less than \(\exp(d^{2/3+\varepsilon })\). This improves on previous results. Of course, this study is related with Lehmer's problem on Mahler measure.
reviewed by: Maurice Mignotte
Mathematics Subject Classification ID: 11R09
zbMATH DE Number: 1466098
zbMATH Keywords: house of a polynomial
author: A. Dubickas
MaRDI profile type: Publication
cites work: Computing the volume is difficult
cites work: Q3474727
cites work: On a conjecture of A. Schinzel and H. Zassenhaus
cites work: On the number of polynomials of bounded measure
cites work: Q3793282
cites work: Q3919790
cites work: A refinement of two theorems of Kronecker
full work available at URL: https://doi.org/10.1007/bf02469281
OpenAlex ID: W2066712619
description: scientific article; zbMATH DE number 1466098