A uniform relative Dobrowolski's lower bound over abelian extensions.

Francesco Amoroso (1) , Umberto Zannier (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 SNS - Scuola Normale Superiore di Pisa

Let L/K be an abelian extension of number fields. We prove an uniform lower bound for the height in L^∗ outside roots of unity. This lower bound depends only on the degree [L : K].

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso, Umberto Zannier. A uniform relative Dobrowolski's lower bound over abelian extensions.. Bulletin of the London Mathematical Society, 2010, 42 (3), pp.489-498. ⟨hal-00424258⟩