Jacob's ladders and new class of integrals containing product of factors $\zeta^2$

TL;DR

This paper explores new properties of the Riemann zeta-function on the critical line and derives an asymptotic formula for a novel class of transcendental integrals involving the zeta-function's squared factors.

Contribution

It introduces a new class of integrals related to the Riemann zeta-function and provides asymptotic formulas for them, expanding understanding of zeta-function properties.

Findings

New properties of the Riemann zeta-function on the critical line

Asymptotic formulas for a novel class of transcendental integrals

Enhanced understanding of integrals involving $\

Abstract

In this paper we obtain new properties of a signal generated by the Riemann zeta-function on the critical line. At the same time we obtain an asymptotic formula for a new class of transcendental integrals connected with the Riemann zeta-function.