On the Riemann Zeta Function and the fractional part of rational powers

TL;DR

This paper explores elementary methods to reveal unexpected links between the Riemann Zeta Function, fractional parts of rational powers, and the Prime Zeta Function, highlighting new mathematical connections.

Contribution

It introduces novel elementary approaches to connect the Riemann Zeta Function with fractional parts of rational powers and the Prime Zeta Function.

Findings

Discovered surprising links between the Riemann Zeta Function and fractional parts of rational powers

Established a connection between the Riemann Zeta Function and the Prime Zeta Function

Revealed new elementary methods for analyzing these relationships

Abstract

Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta Function.