On the value-distribution of logarithmic derivatives of Dirichlet L-functions

Abstract

We shall prove an unconditional basic result related to the value- distributions of {(L′/L)(s, χ)} χ and of {(ζ′/ζ)(s + iτ)} τ, where χ runs over Dirichlet characters with prime conductors and τ runs over R. The result asserts that the expected density function common for these distributions are in fact the density function in an appropriate sense. Under the generalized Riemann hypothesis, stronger results have been proved in our previous articles, but our present result is unconditional.