Potential flow in the critical strip and the Riemann hypothesis

TL;DR

This paper models the Dirichlet eta function in the critical strip as a potential flow of an ideal fluid, providing evidence supporting the Riemann hypothesis by showing no zeros off the critical line.

Contribution

It introduces a novel fluid dynamics analogy to analyze the eta function, offering a new perspective and supporting evidence for the Riemann hypothesis.

Findings

No zeros of the eta function found off the critical line within the critical strip.

The potential flow model aligns with the Riemann hypothesis predictions.

Uses complex potential theory and number theory in a combined approach.

Abstract

We describe the behaviour of the Dirichlet eta function in the critical strip, in terms of the potential flow of an ideal fluid. Using well-known results from complex potential theory and number theory, we show that the Dirichlet eta function has no zeros in the critical strip off the critical line, consistent with the Riemann hypothesis.