Jacob's ladders and the three-points interaction of the Riemann zeta-function with itself

TL;DR

This paper demonstrates a novel relationship between the values of the Riemann zeta-function off the critical line and on the critical line, using Jacob's ladders, establishing an analogue of the Faraday law.

Contribution

It introduces a new method linking zeta-function values on different lines via Jacob's ladders, revealing a three-point interaction.

Findings

Values of |z(70+i0(t))|^2 generate corresponding values of |z(1/2+it)|^2

Establishes an analogue of the Faraday law for the zeta-function

Shows a three-point interaction involving Jacob's ladders and zeta-values

Abstract

It is proved that some set of the values of $|\zeta(\sigma_0+i\vp_1(t))|^2$ on every fixed line $\sigma=\sigma_0>1$ generates a corresponding set of the values of $|\zeta(\frac 12+it)|^2$ on the critical line $\sigma=\frac 12$ (i.e. we have an analogue of the Faraday law).