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Hilbert's irreducibility theorem

Known as: Hilbert irreducibility theorem 
In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert, states that every finite number of irreducible polynomials in a… Expand
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Irreducible polynomial

Papers overview

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2018
2018
Hilbertian fields and Hilbert's irreducibility theorem
Hilbert's irreducibility theorem plays an important role in inverse Galois theory. In this article we introduce Hilbertian fields… Expand
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2016
2016
Explicit Hilbert Irreducibility
Let $P(T,X)$ be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility… Expand
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2010
2010
Hilbert Irreducibility above algberaic groups
The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic… Expand
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2007
2007
Ideal class groups, Hilbert's irreducibility theorem, and integral points of bounded degree on curves
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… Expand
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2000
2000
On a Special Case of Hilbert's Irreducibility Theorem
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… Expand
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1998
1998
Extended Hilbert irreducibility and its applications
We extend the effective Hilbert irreducibility theorem concerning the reduction of a single multivariate polynomial to one… Expand
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Highly Cited
1995
Highly Cited
1995
Effective Noether Irreducibility Forms and Applications
  • E. Kaltofen
  • J. Comput. Syst. Sci.
  • 1995
    • Corpus ID: 13337095
An absolutely irreducible multivariate polynomial is a polynomial that cannot be factored even if the coefficients of the factors… Expand
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1991
1991
Effective Noether irreducibility forms and applications
Using recent absolute irreducibility testing algorithms, we derive new irreducibility forms. These are integer polynomials in… Expand
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1988
1988
Algebraic Extensions in Nonstandard Models and Hilbert's Irreducibility Theorem
Etude des extensions algebriques dans les modeles non standards. Applications a la theorie des nombres. Theoreme d… Expand
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1985
1985
Effective Hilbert Irreducibility
In this paper we prove by entirely elementary means a very effective version of the Hilbert irreducibility theorem. We then apply… Expand
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