On a special case of Hilbert's irreducibility theorem
type: Item
instance of: scholarly article
title: On a special case of Hilbert's irreducibility theorem
zbMATH Open document ID: 0985.12001
author: Marius Cavachi
published in: Journal of Number Theory
publication date: 2002-01-24T00:00:00Z
review text: Let \(K\) be a number field normal over \(\mathbb Q\), and let \(P\) be the set of rational primes that remain prime in \(K\). The author proves the following statement: Let \(f,g\in K[X]\) be two polynomials with no common root. If \(\text{deg }g>\text{deg }f\), then the polynomial \(f+pg\) is reducible for at most finitely many primes \(p\in P\). A similar statement is proved also for polynomials \(f,g\in K[X_1,\dots,X_n]\), under the condition \(\text{deg}_{X_1}g>\text{deg}_{X_1}f\).
reviewed by: Roberto Dvornicich
Mathematics Subject Classification ID: 12E25
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 1538256
zbMATH Keywords: Hilbert's irreducibility theorem
MaRDI profile type: Publication
OpenAlex ID: W2002406301
cites work: On Hilbert's irreducibility theorem
cites work: Q4063245
cites work: Q3490105
DOI: 10.1006/JNTH.1999.2476
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description: scientific article; zbMATH DE number 1538256