An equation satisfied by all non-trivial zeros $ρ$ of the Riemann zeta function $ζ$

Details An equation satisfied by all non-trivial zeros $ρ$ of the Riemann zeta function $ζ$ An equation satisfied by all non-trivial zeros $ρ$ of the Riemann zeta function $ζ$

2009-11-30

arxiv.org/abs/0911.5572v15

Mathematics

General Mathematics

3 pages

Scientific paper

We show that if $\rho$ is a non-trivial zero of the Riemann zeta function
$\zeta$ then $$2^\rho + \frac{1}{\rho - 1} + 1/2 = \rho \int_{1}^{\infty} {t +
1/2} t^{-\rho-1} dt$$ where, ${x}$ is the fractional part of $x$.

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