Aspects of the screw function corresponding to the Riemann zeta function

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.
Comment: 32 pages. The proof of Theorem 1.4 has been revised, and the organization of the paper has been significantly revised in the latest version