19 citations · 71 across the 25 of their papers we have counts for
32 papers
Poincaré-Reeb graphs of real algebraic domains
Arnaud Bodin, Patrick Popescu-Pampu, Miruna-Stefana Sorea
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consists of disjoint smooth connected components of real algebraic plane curves. We stu…
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…
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(…