A short Brownian motion proof of the Riemann hypothesis

TL;DR

This paper presents a concise probabilistic proof of the Riemann hypothesis using Brownian motion, relying on a novel algebraic conjecture relating the Riemann zeta function and a trivial zeta.

Contribution

It introduces a new probabilistic approach to the Riemann hypothesis based on an unexpected algebraic conjecture connecting key zeta functions.

Findings

Probabilistic proof of the Riemann hypothesis

Introduction of the MAC algebraic conjecture

Deep connection between zeta functions

Abstract

We give a short probabilistic (a Brownian motion) proof of the Riemann hypothesis based on some surprising, unexpected and deep algebraic conjecture (MAC in short) concerning the relation between the Riemann zeta $\xi$ and a trivial zeta $\zeta_{t}$. That algebraic conjecture was firstly discovered and formulated in [MA]