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

Justas Kalpokas; Jörn Steuding

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

Number Theory 2009-07-14 v1

Authors: Justas Kalpokas , Jörn Steuding

Abstract

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.

Keywords

riemann zeta-function critical line value distribution riemann hypothesis real values mean value

Cite

@article{arxiv.0907.1910,
  title  = {On the value-distribution of the Riemann zeta-function on the critical line},
  author = {Justas Kalpokas and Jörn Steuding},
  journal= {arXiv preprint arXiv:0907.1910},
  year   = {2009}
}

Comments

16 pages, 1 figure

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