On logarithmic derivatives of zeta functions in families of global fields

Philippe Lebacque (1) , Alexey Zykin (2, 3, 4)

1 UON - University of Nottingham, UK
2 IML - Institut de mathématiques de Luminy
3 ISCP - Interdisciplinary Scientific Center Poncelet
4 Mathematical Institute of the Russian Academy of Sciences

We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reaching generalization of the explicit Brauer-Siegel theorem both for number fields and function fields.

Mots clés: zeta function; families of global fields

Domaines: Théorie des nombres [math.NT]

Philippe Lebacque, Alexey Zykin. On logarithmic derivatives of zeta functions in families of global fields. 2009. ⟨hal-00368945⟩