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).
@article{388,
title = {Applications of uniform distribution theory to the Riemann zeta-function},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v64i0.388},
language = {EN},
url = {http://dml.mathdoc.fr/item/388}
}
Özbek, Selin Selen; Steuding, Jörn. Applications of uniform distribution theory to the Riemann zeta-function. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v64i0.388. http://gdmltest.u-ga.fr/item/388/