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

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 $x$.

💡 Research Summary

The paper under review claims to have discovered a universal equation satisfied by every non‑trivial zero ρ of the Riemann zeta‑function ζ(s). The stated identity is

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