Determinantal approach to a proof of the Riemann hypothesis

TL;DR

This paper explores a determinantal method to prove the Riemann hypothesis, building on previous work and establishing new relations that could advance understanding of this longstanding mathematical problem.

Contribution

It extends prior determinantal approaches to the Riemann hypothesis and introduces new relations across five areas related to the problem.

Findings

Identified conditions under which determinants imply the hypothesis

Extended previous work by Csordas, Norfolk, and Varga

Proposed new conjectures and relations in the determinantal framework

Abstract

We discuss the application of the determinantal method to the proof of the Riemann hypothesis. We start from the fact that, if a certain doubly infinite set of determinants are all positive, then the hypothesis is true. This approach extends the work of Csordas, Norfolk and Varga in 1986, and makes extensive use of the results described by Karlin. We have discovered and proved or conjectured relations in five areas of the problem, as summarized in the Introduction. Further effort could well lead to more progress.