Riemann's Last Theorem

TL;DR

This paper claims to prove Riemann's last theorem by introducing a new form of the zeta function with specific properties that imply all non-trivial zeros lie on the critical line.

Contribution

It presents a novel formulation of the zeta function involving two sub-functions, aiming to prove the Riemann Hypothesis.

Findings

Proposes a new zeta function form with unique properties.

Shows that zeros satisfy an exponential equality only when real part is 1/2.

Concludes that the Riemann Hypothesis is proven.

Abstract

The central idea of this article is to introduce and prove a special form of the zeta function as proof of Riemann's last theorem. The newly proposed zeta function contains two sub functions, namely $f_1(b,s)$ and $f_2(b,s)$. The unique property of $\zeta(s)=f_1(b,s)-f_2(b,s)$ is that as tends toward infinity the equality $\zeta(s)=\zeta(1-s)$ is transformed into an exponential expression for the zeros of the zeta function. At the limiting point, we simply deduce that the exponential equality is satisfied if and only if $\mathfrak{R}(s)=1/2$. Consequently, we conclude that the zeta function cannot be zero if $\mathfrak{R}(s)\ne 1/2$, hence proving Riemann's last theorem.