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Christian Drouin

Publications and source records attributed to Christian Drouin.

4 recordsLinked to original sources
arXiv2026

Solutions of polynomial equations in several variables modulo a prime power

We explain how to obtain the set of solutions of a multivariate polynomial equation modulo a power of a prime number. These solutions are determined by a tree, called the trunk, which makes it possible to reconstruct all solutions. We apply these methods to determine the number of solutions, without having to enumerate them. We also illustrate these techniques by proving a simple case of Igusa's theorem: the Poincar\'e series associated with a polynomial in two separated variables is rational.

math.NT↗
arXiv2024

Around the gcd of the values of two polynomials

We propose a mathematical walk around the gcd of the values $A(n)$ and $B(n)$ of two polynomials evaluated at an integer $n$. This is an opportunity to use a very powerful tool: the resultant.

math.NT↗
arXiv2015

A two-dimensional continued fractions algorithm with Lagrange and Dirichlet properties

A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced from a geometrical quality of the algorithm. Some refercences are given to the works of various authors, in the domain of multidimensional continued fractions algorithms.

math.NT↗