On logarithmic derivatives of zeta functions in families of global fields

2009/03/18 by Lebacque, Philippe, Zykin, Alexey
#11M38 #11R42 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0903.3105

Abstract

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.

Related

• Asymptotic properties of Dedekind zeta functions in families of number fields
• Infinite global fields and the generalized Brauer--Siegel theorem
• Generalized logarithmic derivatives for K_n
• The functional equation of the zeta function of a global field
• Omega theorems for logarithmic derivatives of zeta and L-functions