Numerical Determination of a Certain Mathematical Constant Related to the Mobius Function
Cardinal Stefan Wyszynski University
Faculty of Mathematics and Natural Sciences
ul. Wóycickiego 1/3, PL-01-938 Warsaw, Poland
E-mail: m.wolf@uksw.edu.pl
Received:
Received: 18 April 2023; revised: 16 May 2023; accepted: 17 May 2023; published online: 7 June 2023
DOI: 10.12921/cmst.2023.0000008
Abstract:
We calculated numerically the value of some constant which can be regarded as an analogue of the Euler-Mascheroni constant.
Key words:
convergent and divergent series, Möbius function, Stjelties constants
References:
[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. Mas´lanka, 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. Heath-Brown.
[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).