Are the Stieltjes constants irrational ? : Some computer experiments

• Autorzy: Maślanka K. D. , Wolf M.

Identyfikatory

DOI

10.12921/cmst.2020.0000026

• Języki publikacji: EN

Abstrakty

EN

Khnichin’s theorem is a surprising and still relatively little known result. It can be used as a specific criterion for determining whether or not any given number is irrational. In this paper we apply this theorem as well as the Gauss-Kuzmin theorem to several thousand high precision (up to more than 53 000 significant digits) initial Stieltjes constants γn, n = = 0, 1, 2, . . . , 5000 in order to confirm that, as is commonly believed, they are irrational numbers (and even transcendental). We also study the normality of these important constants.

Słowa kluczowe

EN

Continued fractions; Riemann zeta function; Khinchin’s theorem; experimental mathematics; normality

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2020
• Tom: Vol. 26, No. 3
• Strony: 77--87
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Maślanka K. D.

• Institute for the History of Science, Polish Academy of Sciences ul. Nowy Swiat 72, 00-330 Warsaw, Poland

autor

Wolf M.

• Cardinal Stefan Wyszynski University Faculty of Mathematics and Natural Sciences, College of Sciences ul. Wóycickiego 1/3, 01-938 Warsaw, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).