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

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

2009-07-10

arxiv.org/abs/0907.1910v1

Mathematics

Number Theory

16 pages, 1 figure

Scientific paper

We investigate the intersections of the curve $\mathbb{R}\ni t\mapsto
\zeta({1\over 2}+it)$ 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.

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