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Warianty tytułu
Języki publikacji
Abstrakty
In this article, we develop two types of asymptotic formulas for harmonic series in terms of single non-trivial zeros of the Riemann zeta function on the critical line. The series is obtained by evaluating the complex magnitude of an alternating and non-alternating series representation of the Riemann zeta function. Consequently, if the asymptotic limit of the harmonic series is known, then we obtain the Euler-Mascheroni constant with log(k). We further numerically compute these series for different non-trivial zeros. We also investigate a recursive formula for non-trivial zeros.
Rocznik
Tom
Strony
161--166
Opis fizyczny
Bibliogr. 5 poz., tab.
Twórcy
Bibliografia
- [1] H.M. Edwards, Riemann’s Zeta Function, Dover Publication, Mineola, New York, 1974.
- [2] J. Havil, Gamma: Exploring Euler’s Constant, Princeton University Press, 2003.
- [3] A. Ivic,´ The Riemann Zeta-Function: Theory and Applications, Dover Publication, Mineola, New York, 1985.
- [4] LMFDB- The L-functions and Modular Forms Database, http://www.lmfdb.org/, 2019.
- [5] M. Wolf, 6+ infinity new expressions for the Euler-Mascheroni constant, math.NT/1904.09855, 2019.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3bf28dbd-19c4-4b23-a766-77129747d0bb