On the value-distribution of the Riemann zeta-function on the critical line

Abstract

We investigate the intersections of the curve $\mathbb{R}\ni t\mapsto \zeta (\frac{1}{2}+it)$ with the real axis. We show that if the Riemann hypothesis is true, the mean-value of those real values exists and is equal to 1. Moreover, we show unconditionally that the zeta-function takes arbitrarily large real values on the critical line.

16 pages, 1 figure

References in corpus (1)

• Extreme values of zeta and L-functions