Aspects of the screw function corresponding to the Riemann zeta function

TL;DR

This paper introduces a screw function linked to the Riemann zeta function, exploring its properties and deriving conditions equivalent to the Riemann hypothesis, including analogs of Weil's positivity and Li's criterion.

Contribution

It presents a novel screw function associated with the Riemann zeta function and establishes new equivalent conditions for the Riemann hypothesis.

Findings

Several equivalent conditions for the Riemann hypothesis

An analog of Weil's positivity and Li's criterion

Partial unconditional results for these conditions

Abstract

We introduce a screw function corresponding to the Riemann zeta-function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so-called Weil's positivity or Li's criterion. In addition, we prove a few partial but unconditional results for such equivalents.