Bill Allombert

An efficient algorithm for the computation of Galois automorphisms

We describe an algorithm for computing the Galois automorphisms of a Galois extension which generalizes the algorithm of Acciaro and Kluners to the non-Abelian case. This is much faster in practice than algorithms based on LLL or factorization.

CM-Points on Straight Lines

We prove that, with “obvious” exceptions, a CM-point \((j(\tau _{1}),j(\tau _{2}))\) cannot belong to a straight line in \(\mathbb{C}^{2}\) defined over \(\mathbb{Q}\). This generalizes a result of Kuhne, who proved this for the line \(x_{1} + x_{2} = 1\).

Euler's divergent series and an elementary model in Statistical Physics

We discuss the multiple integral of a multivariate exponential taken with respect either to the Lebesgue measure or to the discrete uniform Bernoulli measure. In the first case the integral is linked to Eulers everywhere divergent power series and its generalizations, while in the second case the integral is linked to a one-dimensional model of spin systems as encountered in physics.