The screw line of the Riemann zeta-function and its applications

TL;DR

This paper explores the screw line related to the Riemann zeta-function under the Riemann hypothesis, providing new conditions that characterize the hypothesis and explaining the Weil distribution's non-negativity through the norm.

Contribution

It introduces three new necessary and sufficient conditions for the Riemann hypothesis based on the screw line and Weil distribution analysis.

Findings

Derived three conditions equivalent to the Riemann hypothesis

Connected the non-negativity of Weil distribution to the norm

Provided new geometric insights into the zeta-function

Abstract

We investigate the screw line corresponding to the screw function associated with the Riemann zeta-function under the Riemann hypothesis and derive three necessary and sufficient conditions for the Riemann hypothesis as applications. One of them explains the non-negativity of the Weil distribution by means of the norm.