Riemann hypothesis and some new asymptotically multiplicative integrals which contain the remainder of the prime-counting function $\pi(x)$

TL;DR

This paper introduces a new parametric integral derived from the Riemann hypothesis, highlighting its asymptotic multiplicative property and its relation to the prime-counting function's remainder.

Contribution

It presents a novel integral with asymptotic multiplicability linked to the Riemann hypothesis and the prime-counting function.

Findings

New parametric integral related to the Riemann hypothesis

Asymptotic multiplicability property established

Connections to the prime-counting function's remainder

Abstract

A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.