Nearest neighbor spacing distributions for zeros of the real or imaginary part of the Riemann xi-function on vertical lines

TL;DR

This paper investigates the statistical distribution of spacings between zeros of the real or imaginary parts of the Riemann xi-function on vertical lines, linking them to the M-function from the value distribution of the zeta-function's logarithmic derivative.

Contribution

It establishes a connection between the zeros' spacing distributions and the M-function, providing a new perspective on the statistical properties of these zeros.

Findings

Spacing distributions are described by the M-function.

Connection to the value distribution of the zeta-function's derivative.

Provides insights into the zeros' statistical behavior.

Abstract

We show that the density functions of nearest neighbor spacing distributions for zeros of the real or imaginary part of the Riemann xi-function on vertical lines are described by the M-function which is appeared in value distributions of the logarithmic derivative of the Riemann zeta-function on vertical lines.