Jacob's ladders and some nonlinear integral equations connected with the Poisson-Lobachevsky integral

TL;DR

This paper explores new properties of the Riemann zeta-function signal, establishing a connection with a nonlinear integral equation linked to the Poisson-Lobachevsky integral, advancing understanding in analytic number theory.

Contribution

It introduces a novel relationship between the Riemann zeta-function and a specific nonlinear integral equation associated with the Poisson-Lobachevsky integral.

Findings

New properties of the Riemann zeta-function signal

Connection between zeta-function and nonlinear integral equations

Insights into Poisson-Lobachevsky integral relations

Abstract

We obtain some new properties of the signal generated by the Riemann zeta-function in this paper. Namely, we show the connection between the function $\zf$ and a nonlinear integral equation related to the Poisson-Lobachevsky integral.