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Mathematics  2008 

A necessary condition for the existence of the nontrivial zeros of the Riemann zeta function

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Abstract:

Starting from the symmetrical reflection functional equation of the zeta function, we have found that the sigma values satisfying zeta(s) = 0 must also satisfy |zeta(s)| = |zeta(1 - s)|. The sigma values satisfying this requirement are a necessary condition for the existence of the nontrivial zeros. We have shown that sigma = 1/2 is the only numeric solution that satisfies the requirement.

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