# An application of Titchmarsh's theorem and the Salem equivalence

## TL;DR

This paper explores the extension of Salem-type equivalences related to the Riemann hypothesis using Titchmarsh's theorem, providing new insights into Fourier integrals and their connection to the hypothesis.

## Contribution

It introduces an extension of Salem's equivalence for the Riemann hypothesis through the application of Titchmarsh's theorem, offering novel theoretical connections.

## Key findings

- Extended Salem equivalence using Titchmarsh's theorem
- New notes on Fourier integrals related to the hypothesis
- Additional equivalences to the Riemann hypothesis

## Abstract

We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fourier integrals are provided.