Number Theory


Riemann's Analytic Continuation of Zeta(s) Contradicts the Law of the Excluded Middle, and is Derived by Using Cauchy's Integral Theorem While Contradicting the Theorem's Prerequisites

Authors: Ayal Sharon

The Law of the Excluded Middle holds that either a statement "X" or its opposite "not X" is true. In Boolean algebra form, Y = X XOR (not X). Riemann's analytic continuation of Zeta(s) contradicts the Law of the Excluded Middle, because the Dirichlet series Zeta(s) is proven divergent in the half-plane Re(s)<=1. Further inspection of the derivation of Riemann's analytic continuation of $\zeta(s)$ shows that it is wrongly based on the Cauchy integral theorem, and thus false.

Comments: 11 Pages.

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[v1] 2018-02-19 17:14:55

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