Asymptotic formulas for harmonic series in terms of a non-trivial zero on the critical line

• Autorzy: Kawalec A.

Identyfikatory

DOI

10.12921/cmst.2019.0000047

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Riemann zeta function; harmonic series; Euler-Mascheroni constant; non-trivial zeros

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2019
• Tom: Vol. 25, No. 4
• Strony: 161--166
• Opis fizyczny: Bibliogr. 5 poz., tab.

Twórcy

autor

Kawalec A.

• 214 W Jennifer Ln, #6 Palatine, IL 60067, USA

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).