16 citations · 18 across the 13 of their papers we have counts for
19 papers · 1 filter
Integral Specializations of Polynomials: Hilbert Irreducibility, Coprimality, and Density
Angelot Behajaina, Pierre Dèbes, Martin Widmer
The Hilbert specialization property of a field, whereby irreducibility of polynomials is preserved under specialization of some of the variables, admits an integral counterpart whe…
Hurwitz spaces and Inverse Galois Theory
Pierre Dèbes
Hurwitz spaces which parametrize branched covers of the line play a prominent role in inverse Galois theory. This paper surveys fifty years of works in this direction with emphasis…
Integrally Hilbertian rings and the polynomial Schinzel hypothesis
Angelot Behajaina, Pierre Dèbes, Joachim König
The classical Hilbert specialization property is a field-theoretic tool ensuring that polynomial irreducibility over a field is preserved under specialization of some of the variab…
Improvements on dimension growth results and effective Hilbert's irreducibility theorem
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel +2
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree , over any global field. In…
Polynomial equations modulo prime numbers
Arnaud Bodin, Pierre Dèbes, Salah Najib
We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers . We offer an elementary approach based on a counting metho…
Coprime values of polynomials in several variables
Arnaud Bodin, Pierre Dèbes
Given two polynomials , in one or more variables and with integer coefficients, how does the property that they are coprime relate to their value…