Some remarks on the Báez-Duarte criterion for the Riemann hypothesis

• Autorzy: Wolf M.

Identyfikatory

DOI

10.12921/cmst.2014.20.02.39-47

• Języki publikacji: EN

Abstrakty

EN

In this paper we are going to describe the results of the computer experiment, which in principle can rule out validity of the Riemann Hypothesis (RH). We use the sequence ck appearing in the Báez-Duarte criterion for the RH and compare two formulas for these numbers. We describe the mechanism of possible violation of the Riemann Hypothesis. Next we calculate c100000 with a thousand digits of accuracy using two different formulas for ck with the aim to disprove the Riemann Hypothesis in the case these two numbers will differ. We found the discrepancy only on the 996th decimal place (accuracy of 10-996). The computer experiment reported herein can be of interest for developers of Mathematica and PARI/GP.

Słowa kluczowe

EN

Riemann hypothesis; zeta function; Baez-Duarte criterion

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2014
• Tom: Vol. 20, No. 2
• Strony: 39--47
• Opis fizyczny: Bibliogr. 41 poz., rys.

Twórcy

autor

Wolf M.

• Cardinal Stefan Wyszynski University Faculty of Mathematics and Natural Sciences. College of Sciences ul. Wóycickiego 1/3, Auditorium Maximum, (room 113) PL-01-938 Warsaw, Poland

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