On the Triviality of Solutions of a Salem-Type Integral Equation and Its Connection with the Riemann Hypothesis

TL;DR

This paper claims to prove the Riemann Hypothesis by analyzing a Salem-type integral equation and showing it has only the trivial solution within a certain function class.

Contribution

It introduces a novel approach linking a Salem-type integral equation to the Riemann Hypothesis and proves the triviality of solutions in that context.

Findings

The integral equation admits only the trivial solution for bounded and measurable functions.

The approach provides a new perspective on the Riemann Hypothesis through integral equations.

The paper establishes a connection between Salem-type equations and the Riemann Hypothesis.

Abstract

In this paper we prove the Riemann Hypothesis. More precisely, we study a Salem-type linear Fredholm integral equation of the first kind with symmetric kernel and prove that, in the class of bounded and measurable functions, this equation admits only the trivial solution.