Applications of uniform distribution theory to the Riemann zeta-function

Abstract

We give two applications of uniform distribution theory to the Riemann zeta-function. We show that the values of the argument of $\zeta({1\over 2}+iP(n))$ are uniformly distributed modulo ${\pi \over 2}$ where $P(n)$ denotes the values of a polynomial with real coefficients evaluated at the positive integers. Moreover, we study the distribution of $\arg\zeta'({1\over 2}+i\gamma_n)$ modulo $\pi$ where $\gamma_n$ is the $n$th ordinate of a zeta zero in the upper half-plane (in ascending order).