Nontrivial Zeroes of Riemann Zeta Function are Symmetrical with respect to Critical Line

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Theorem

The nontrivial zeroes of the Riemann $\zeta$ function are distributed symmetrically with respect to the critical line.

That is, suppose $s_1 = \sigma_1 + i t$ is a nontrivial zero of $\zeta$.

Then there exists another nontrivial zero $s_2$ of $\zeta$ such that:

$s_2 = 1 - \sigma_1 + i t$


Proof




Also see


Sources