A proof of Lindel\"of's hypothesis

TL;DR

This paper introduces a new Lindel"of-function related to the zeta function ratio, and uses its properties to prove Lindel"of's hypothesis, advancing understanding of the zeta function's growth.

Contribution

It provides a novel extension of Lindel"of's function and a proof of Lindel"of's hypothesis based on this new framework.

Findings

Established a unique extension of Lindel"of's function

Proved Lindel"of's hypothesis using the extended function

Linked the ratio of zeta functions to the hypothesis

Abstract

We define an associated Lindel\"of-function for the ratio of the zeta functions and use its representation to get a unique extension of Lindel\"of's function that proves Lindel\"of's hypothesis.