The zeros of the Riemann-zeta function and the transition from pseudo-random to harmonic behavior

TL;DR

This paper introduces a new function derived from the Riemann-zeta zeros that transitions from pseudo-random to harmonic behavior as its argument increases, revealing new insights into the zeros' structure.

Contribution

It proposes a novel function based on Riemann-zeta zeros and characterizes its transition from pseudo-random to harmonic behavior with increasing argument.

Findings

Function exhibits a transition from pseudo-random to harmonic behavior

Frequency of harmonic behavior decreases with increasing argument

Provides new perspective on the distribution of Riemann-zeta zeros

Abstract

In this work, it is introduced a new function based on the non-trivial zeros of the Riemann-zeta function. Such function shows an interesting behavior: when the argument of the function grows, it changes from a pseudo-random behavior to a harmonic behavior with decreasing frequency.