Room 327

Galois Groups of lacunray polynomials are large

Sinnou David

Sorbonne University (Paris 6)

We show that the Galois group defined by the roots of a lacunary polynomial is large in the sense that it grows faster than polynomially with de degree. Lacunary polynomials are the standard way of producing examples of algebraic numbers with small Weil height. One of the key tools is to use a lower bound for the height of a point of $\gu_m^n$ over the maximal abelian extension proven earlier by Delsinne.