Fourier coefficients associated with the Riemann zeta-function

Yu.V. Basiuk; S.I. Tarasyuk

doi:10.15330/cmp.8.1.16-20

Fourier coefficients associated with the Riemann zeta-function

Authors

Yu.V. Basiuk Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine https://orcid.org/0000-0002-6141-8975
S.I. Tarasyuk Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine

https://doi.org/10.15330/cmp.8.1.16-20

Keywords:

Fourier coefficients, the Riemann zeta-function, Riemann Hypothesis

Published online: 2016-06-30

Abstract

We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation. Also we obtain a new restatement of the Riemann Hypothesis.