Fourier coefficients associated with the Riemann zeta-function

Yu. V. Basiuk, S. I. Tarasyuk

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.


Keywords


Fourier coefficients, the Riemann zeta-function, Riemann Hypothesis

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