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arXiv · 1109.2224

Negative values of the Riemann zeta function on the critical line

Justas Kalpokas·Maxim A. Korolev·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 unconditionally that the zeta-function takes arbitrarily large positive and negative values on the critical line.

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Justas Kalpokas, Maxim A. Korolev, Jörn Steuding. 2012-05-15. Negative values of the Riemann zeta function on the critical line. https://doi.org/10.1112/s0025579313000090

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