Some Order-Theoretic Properties of the Zeros of the Zeta Function

TL;DR

This paper investigates the order-theoretic structure of the non-trivial zeros of the zeta function, revealing properties of minimal elements within the partially ordered set defined by coordinatewise order.

Contribution

It introduces a novel order-theoretic perspective on the zeros of the zeta function and proves new properties about their minimal elements.

Findings

Identification of properties of minimal elements in the zero set

Insights into the structure of zeros under coordinatewise order

Advancement in understanding the zeros' arrangement

Abstract

The (partially) ordered set of the non-trivial zeros of the zeta function with positive imaginary parts is considered. The order is the coordinatewise order inherited from $\mathbb{C}$. Some interesting properties regarding the minimal elements of this poset are proven.