Simultaneous distribution of fractional parts of Riemann zeta zeros

TL;DR

This paper studies how the fractional parts of scaled Riemann zeta zeros are distributed simultaneously for multiple fixed parameters, revealing insights into their joint distribution properties.

Contribution

It introduces a new analysis of the joint distribution of fractional parts of Riemann zeta zeros scaled by multiple fixed real numbers.

Findings

Distribution patterns depend on the fixed parameters

Results extend understanding of zeta zeros' fractional parts

Provides groundwork for future distribution studies

Abstract

We investigate the simultaneous distribution of the fractional parts of $\{\alpha_1 \gamma, \alpha_2\gamma, \cdots, \alpha_n\gamma\}$, where $n\geq 2$, $\alpha_1$, $\alpha_2$, $\ldots$, $\alpha_n$ are fixed, distinct positive real numbers and $\gamma$ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta-function.