Jacob's ladders and some generalizations of certain Ramachandra's inequality

TL;DR

This paper generalizes Ramachandra's inequality to provide new lower bounds for the energies of complex signals derived from the Riemann zeta-function on the critical line, advancing understanding in analytic number theory.

Contribution

It introduces novel generalizations of Ramachandra's inequality, offering improved lower estimates for the energies associated with signals from the Riemann zeta-function.

Findings

New lower bounds for energies of signals from the Riemann zeta-function

Generalizations of Ramachandra's inequality

Enhanced estimates on the behavior of the zeta-function on the critical line

Abstract

In this paper we obtain some essential generalizations of certain Ramachandra's inequality, i. e. we obtain new lower estimates for the energies of some complicated signals generated by the Riemann zeta-function on the critical line.