# Seminars

Regular seminars are held on Thursdays in the Kapitza Institute in Moscow and on Fridays at the scientific council of the Landau Institute in Chernogolovka.

Departments of the institute hold their own seminars; the topic are determined by the scientific orientation of the related department.

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## Zeros of Riemann’s Zeta Functions in the Line z=1/2+it_{0}

18 September in 11:30 at scientific council

Yu.N. Ovchinnikov

Investigation of Josephson effect, current flow in narrow superconducting stripes, dynamical states in superconductors lead to the necessity to deal with an important phenomenon: phase slip events. The study of the distribution of zeros for Riemann's Zeta function also requires an analisis of the same phenomenon.

It was found that, in addition to trivial zeros in points ($ z = -2N, N = 1, 2, ... $, natural numbers), the Riemann’s zeta function $\zeta(z)$ has zeros only on the line {$z = 1/2 + i t_0$, $t_0$ is real}. All zeros are numerated, and for each number, N, the positions of the non-overlap intervals with one zero inside are found. The simple equation for the determination of centers of intervals is obtained. The analytical function $\eta(z)$), leading to the possibility fix the zeros of the zeta function $\zeta(z)$, was estimated. To perform the analysis, the well-known phenomenon, phase-slip events, is used. This phenomenon is the key ingredient for the investigation of dynamical processes in solid-state physics, for example, if we are trying to solve the TDGLE (time-dependent Ginzburg-Landau equation).

J. Supercond. Novel Magn., 32(11), 3363-3368 (2019)

It was found that, in addition to trivial zeros in points ($ z = -2N, N = 1, 2, ... $, natural numbers), the Riemann’s zeta function $\zeta(z)$ has zeros only on the line {$z = 1/2 + i t_0$, $t_0$ is real}. All zeros are numerated, and for each number, N, the positions of the non-overlap intervals with one zero inside are found. The simple equation for the determination of centers of intervals is obtained. The analytical function $\eta(z)$), leading to the possibility fix the zeros of the zeta function $\zeta(z)$, was estimated. To perform the analysis, the well-known phenomenon, phase-slip events, is used. This phenomenon is the key ingredient for the investigation of dynamical processes in solid-state physics, for example, if we are trying to solve the TDGLE (time-dependent Ginzburg-Landau equation).

J. Supercond. Novel Magn., 32(11), 3363-3368 (2019)