Asymptotic properties of Dedekind zeta functions in families of number fields

Alexey Zykin (1)

1 ISCP - Interdisciplinary Scientific Center Poncelet

The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer--Siegel theorem. As an application we obtain a limit formula for Euler--Kronecker constants in families of number fields.

Domaines: Théorie des nombres [math.NT]

Alexey Zykin. Asymptotic properties of Dedekind zeta functions in families of number fields. 2009. ⟨hal-00437935⟩