Hypothesis of Riemann is rejected by definition

TL;DR

This paper argues that the Riemann Hypothesis is invalid by definition, claiming that the zeta function's zeros do not satisfy the assumed equalities for all related functions, challenging a fundamental mathematical conjecture.

Contribution

It presents a novel argument that the Riemann Hypothesis is false by showing the zero conditions do not hold universally for related functions.

Findings

Riemann Hypothesis is rejected by definition.

The equality R(s) = 1/2 does not hold for all related functions.

The hypothesis fails for certain generalized zeta functions.

Abstract

Hypothesis of Riemann is rejected by definition, because {\zeta}(s), where s zeros of {\zeta}(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/2 holds only for the zeros of {\zeta}(s) = 0 and for the zeros of certain related functions. However, it does not hold for certain special generalized functions of {\zeta}(), such the Zeta Hurwitz functions and their sums.