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).
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).
