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NEGATIVE VALUES OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  17 June 2013

Justas Kalpokas ,
Maxim A. Korolev  and
Jörn Steuding
Justas Kalpokas
Affiliation:
Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius,Lithuania email justas.kalpokas@mif.vu.lt
Maxim A. Korolev
Affiliation:
Steklov Mathematical Institute, Gubkina str. 8, 119991 Moscow,Russia email hardy_ramanujan@mail.ru, korolevma@mi.ras.ru
Jörn Steuding
Affiliation:
Department of Mathematics, Würzburg University, Am Hubland, 97218 Würzburg,Germany email steuding@mathematik.uni-wuerzburg.de
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Abstract

We investigate the intersections of the curve $ \mathbb{R} \ni t\mapsto \zeta (\frac{1}{2} + \mathrm{i} t)$ with the real axis. We show unconditionally that the zeta function takes arbitrarily large positive and negative values on the critical line.

MSC classification

Secondary: 11M06: $zeta (s)$ and $L(s, chi)$
Type
Research Article
Information
Mathematika , Volume 59 , Issue 2 , July 2013 , pp. 443 - 462
Copyright
Copyright © University College London 2013 

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