Mahler measure on Galois extensions

Francesco Amoroso (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We study the Mahler measure of generators of a Galois extension with Galois group the full symmetric group. We prove that two classical constructions of generators gives always algebraic numbers of big height. These results answer a question of C. Smyth and provide some evidence to a conjecture which asserts that the height of such a generator growth to infinity with the degree of the extension.

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso. Mahler measure on Galois extensions. Bulletin of the London Mathematical Society, 2016. ⟨hal-01575925⟩