Algebraic Numbers of Small Weil's Height in CM fields: on a Theorem of Schinzel

Francesco Amoroso (1) , Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

Let S be the union of all CM-fields and S_0 be the set of non-zero algebraic numbers of S which are not roots of unity. We show that in S_0 Weil's height cannot be bounded from below by an absolute constant.

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio. Algebraic Numbers of Small Weil's Height in CM fields: on a Theorem of Schinzel. Journal of Number Theory, 2006, 122, pp.247-260. ⟨hal-00947162⟩