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Riemann's Last Theorem

Published 28 Dec 2021 in math.GM | (2201.00615v2)

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 f1(b,s)f_1(b,s) and f2(b,s)f_2(b,s). The unique property of ζ(s)=f1(b,s)−f2(b,s)\zeta(s)=f_1(b,s)-f_2(b,s) is that as tends toward infinity the equality ζ(s)=ζ(1−s)\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 R(s)=1/2\mathfrak{R}(s)=1/2. Consequently, we conclude that the zeta function cannot be zero if R(s)≠1/2\mathfrak{R}(s)\ne 1/2, hence proving Riemann's last theorem.

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