A simple numerical approach to the Riemann hypothesis

  • The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.

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Author:Nikolai Tarkhanov
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1 (2012) 9)
Document Type:Preprint
Date of Publication (online):2012/01/18
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/01/18
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:11-XX NUMBER THEORY / 11Mxx Zeta and L-functions: analytic theory / 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheses
11-XX NUMBER THEORY / 11Mxx Zeta and L-functions: analytic theory
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990 , SK 180