Integral operators arising from the Riemann zeta function

TL;DR

This paper explores integral operators linked to the Riemann zeta function, describing their determinants and introducing new operators with analyzed properties, advancing understanding of their mathematical structure.

Contribution

It provides a novel representation of Fredholm determinants for zeta-related operators and introduces a new integral operator with studied analytic features.

Findings

Expressed a ratio of Fredholm determinants via a single integral equation

Introduced a new integral operator from the Riemann zeta function

Analyzed the basic analytic properties of the new operator

Abstract

In this paper we have two issues coming from the same background. The first one is to describe a certain ratio of Fredholm determinants of integral operators arising from the Riemann zeta function by using the solution of a single integral equation. The second one is to introduce a new integral operator arising from the Riemann zeta function and to study its basic analytic properties.