16 citations · 19 across the 6 of their papers we have counts for
7 papers · 1 filter
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…
The Hilbert-Schinzel specialization property
Arnaud Bodin, Pierre Dèbes, Joachim König +1
We establish a version "over the ring" of the celebrated Hilbert Irreducibility Theorem. Given finitely many polynomials in variables, with coefficients in , of po…
The relative Schinzel hypothesis
Arnaud Bodin, Pierre Dèbes, Salah Najib
The Schinzel Hypothesis is a conjecture about irreducible polynomials in one variable over the integers: under some standard condition, they should assume infinitely many prime val…
Prime and coprime values of polynomials
Arnaud Bodin, Pierre Dèbes, Salah Najib
The Schinzel Hypothesis is a celebrated conjecture in number theory linking polynomial values and prime numbers. In the same vein we investigate the common divisors of values $P_1(…
The Schinzel Hypothesis for Polynomials
Arnaud Bodin, Pierre Dèbes, Salah Najib
The Schinzel hypothesis is a famous conjectural statement about primes in value sets of polynomials, which generalizes the Dirichlet theorem about primes in an arithmetic progressi…
Noether's forms for the study of non-composite rational functions and their spectrum
Laurent Busé, Guillaume Chèze, Salah Najib
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. Wit…