Théorème de Chebotarev effectif

Bruno Winckler (1)

1 Équipe Théorie des Nombres

Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic integral as x tends to infinity, and these automorphisms are well-distributed among the conjugacy classes of G : this is the Chebotarev theorem. The purpose of this paper is to compute the absolute constants of the error term appearing in a previous work about this theorem, due to Lagarias and Odlyzko.

Mots clés: prime ideals; chebotarev; density theorem; zeta-function

Domaines: Théorie des nombres [math.NT]

Bruno Winckler. Théorème de Chebotarev effectif. 2013. ⟨hal-00907410⟩