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Effectivité dans le théorème d'irréductibilité de Hilbert

Abstract : Hilbert's irreducibility theorem gives the existence of a specialization preserving the irreducibility of a multivariate polynomial with rational coefficients. Effective versions have been given by P. Dèbes (1993) and by A. Schinzel and U. Zannier (1995). We discuss some attempts to improve these effective results : Dörge's method, congruence method inspired by an article of M. Fried and finally the use of a recent result of R. Heath-Brown about rational points on curves. This last attempt leads to a significant improvement of known results. We also give an application to the research of an algorithm for the factorization of bivariate polynomials.
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Contributor : Yann Walkowiak <>
Submitted on : Tuesday, February 8, 2005 - 10:36:48 AM
Last modification on : Sunday, November 29, 2020 - 3:24:05 AM
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  • HAL Id : tel-00008392, version 1



Yann Walkowiak. Effectivité dans le théorème d'irréductibilité de Hilbert. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2004. Français. ⟨tel-00008392⟩



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