Two Arguments that the Nontrivial Zeros of the Riemann Zeta Function are Irrational

• Autorzy: Wolf M.

Identyfikatory

DOI

10.12921/cmst.2018.0000049

• Języki publikacji: EN

Abstrakty

EN

We have used the first 2600 nontrivial zeros γl of the Riemann zeta function calculated with 1000 digits accuracy and developed them into the continued fractions. We calculated the geometrical means of the denominators of these continued fractions and for all cases we get values close to the Khinchin’s constant, which suggests that γl are irrational. Next we have calculated the n-th square roots of the denominators Qn of the convergents of the continued fractions obtaining values close to the Khinchin-Lévy constant, again supporting the common opinion that γl are irrational.

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: 2018
• Tom: Vol. 24, No. 4
• Strony: 215--220
• Opis fizyczny: Bibliogr. 24 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

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).