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arXiv · 0907.1910

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

Justas Kalpokas·Jörn Steuding
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Abstract

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.

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Justas Kalpokas, Jörn Steuding. 2009-07-10. On the value-distribution of the Riemann zeta-function on the critical line. https://arxiv.org/abs/0907.1910

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