Fourier coefficients associated with the Riemann zeta-function - Basiuk, Yu.V.; Tarasyuk, S.I. (Carpathian Mathematical Publications, 2016)
We study the Riemann zeta-function $ζ(s)$ by a Fourier series method. The summation of $\log|ζ(s)|$ with the kernel $1/|s|^{6}$ on the critical line $Re\; s = \frac{1}{2}$ is the main result of our investigation. Also we obtain a new restatement of the Riemann Hypothesis.