Numerical Determination of a Certain Mathematical Constant Related to the Möbius Function

• Autorzy: Wolf Marek

Identyfikatory

DOI

10.12921/cmst.2023.0000008

• Języki publikacji: EN

Abstrakty

EN

We calculated numerically the value of some constant which can be regarded as an analogue of the EulerMascheroni constant

Słowa kluczowe

EN

Möbius function; convergent series; divergent series; Stieltjes constants

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2023
• Tom: Vol. 29, No. 1-4
• Strony: 17--20
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Wolf Marek

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

Bibliografia

• [1] T.M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York (2010). Undergraduate Texts in Mathematics.
• [2] R.G. Ayoub, An Introduction to the Analytic Theory of Numbers, AMS (2006).
• [3] W.E. Briggs, S. Chowla, The power series coefficients of ζ(s), The American Mathematical Monthly 62(5), 323–325 (1955).
• [4] J.B. Christopher, The asymptotic density of some k-dimensional sets, American Mathematical Monthly 63, 399 (1956).
• [5] G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, Oxford Science Publications (1980).
• [6] J. Havil, Gamma: Exploring Euler’s Constant, Princeton University Press, Princeton, NJ (2003).
• [7] J.C. Lagarias, Euler’s constant: Euler’s work and modern developments, Bulletin of the American Mathematical Society 50(4), 527–628 (2013).
• [8] K. Maslanka, M. Wolf, ´ Are the Stieltjes constants irrational? Some computer experiments, Computational Methods in Science and Technology 26(3), 77–87 (2020).
• [9] PARI/GP, version 2.3.0, 64 bits (2018). Available from http://pari.math.u-bordeaux.fr/.
• [10] W. Rudin, Principles of mathematical analysis, McGraw-Hill Book Co., New York, 3rd ed. (1976). International Series in Pure and Applied Mathematics.
• [11] J. Sondow, Criteria for Irrationality of Euler’s Constant, Proceedings of the American Mathematical Society 131(11), 3335–3345 (2003).
• [12] E.C. Titchmarsh, The Theory of the Riemann Zeta-function, The Clarendon Press Oxford University Press, New York, 2nd ed. (1986). Edited and with a preface by D.R. HeathBrown.
• [13] M. Wolf, Some remarks on the Báez-Duarte criterion for the Riemann Hypothesis, Computational Methods in Science and Technology 20(2), 39–47 (2014).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).