arXiv subjects
Publications and source records attributed to Justas Kalpokas.
We investigate the intersections of the curve $\mathbb{R}\ni t\mapsto ζ({1\over 2}+it)$ with the real axis. We show unconditionally that the zeta-function takes arbitrarily large positive and negative values on the critical line.
We investigate the intersections of the curve $\mathbb{R}\ni t\mapsto ζ({1\over 2}+it)$ 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.