Existence of a zero-free strip for the Riemann zeta function

TL;DR

This paper links recent quantum computer science breakthroughs to the Riemann zeta function, showing that the zeroes' real parts are bounded away from one using advanced representation theory and modular functions.

Contribution

It introduces a novel connection between quantum computational phenomena and number theory, specifically establishing a zero-free region for the Riemann zeta function.

Findings

Supremum of zeroes' real parts is less than one.

Introduces the charged mean ergodic theorem in representation theory.

Constructs new modular functions called complete electromagnetic functions.

Abstract

In a recent article a breakthrough was made in quantum computer science which established the existence of a phenomenon commonly known as $\mathsf{MIP}^\ast = \mathsf{RE}$. We show that the existence of this phenomenon implies that the supremum of the real parts of the zeroes of the Riemann zeta function is less than one. Our main tool is an assertion about the representation theory of the rank two free group that we refer to as the charged mean ergodic theorem. Our method also involves the construction of novel modular functions we refer to as complete electromagnetic functions.