Omega theorems for logarithmic derivatives of zeta and $L$-functions

Abstract

We establish several new $\Omega$-theorems for logarithmic derivatives of the Riemann zeta function and Dirichlet $L$-functions. In particular, this improves on earlier work of Landau (1911), Bohr-Landau (1913), and recent work of Lamzouri.

arXiv commentVersion 2: 24 pages. New results (Theorem 1.7, 1.8) added; new conjectures and problems added in the final section