On the number of roots of an integral polynomial modulo \(q\)
type: Item
instance of: scholarly article
title: On the number of roots of an integral polynomial modulo \(q\)
zbMATH Open document ID: 0916.11015
author: Monique Branton
author: Olivier Ramaré
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1999-06-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/227585
full work available at URL: jtnb1998-1.html
review text: The authors prove that the set of congruence classes modulo a power of a prime number which are roots of an integral polynomial with degree \(d\) is a collection of at most \(d\) arithmetical progressions. This result implies an upper bound on the number of these roots lying in a given small interval; such bounds are useful to study the number of points close to a smooth algebraic curve. The methods of proofs are combinatorial and make no use of Hensel's Lemma.
reviewed by: Maurice Mignotte
Mathematics Subject Classification ID: 11C08
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 11B25
zbMATH DE Number: 1229651
zbMATH Keywords: roots of polynomials
zbMATH Keywords: congruences
zbMATH Keywords: arithmetical progressions
MaRDI profile type: Publication
OpenAlex ID: W2332407780
cites work: Q3912646
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DOI: 10.5802/JTNB.222
description: scientific article; zbMATH DE number 1229651