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2016

2016

Let $P(T,X)$ be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility…

2010

2010

The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic…

Review

2009

Review

2009

We discuss the Hilbert Irreducibility Theorem, presenting briefly a new approach which leads to novel conclusions, especially in…

2007

2007

R´´ Nousla construction et le comptage, pour tout couple d'entiers m,n > 1, des corps de nombres de degre n dont le groupe des…

2002

2002

This paper deals with generalizations of Hilbert's irreducibility theorem. The classical Hilbert irreducibility theorem states…

2000

2000

Abstract We prove that if K is a finite extension of Q , P is the set of prime numbers in Z that remain prime in the ring R of…

1998

1998

We extend the effective Hilbert irreducibility theorem concerning the reduction of a single multivariate polynomial to one…

1988

1988

Etude des extensions algebriques dans les modeles non standards. Applications a la theorie des nombres. Theoreme d…

1985

1985

In this paper we prove by entirely elementary means a very effective version of the Hilbert irreducibility theorem. We then apply…

1982

1982

Algorithms for factoring polynomials in one or more variables over various coefficient domains are discussed. Special emphasis is…