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=
\sum_{p,m}\frac{\log(p)}{p^{m/2}} (F(\log(p^m)+F(-\log(p^m)) -\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi(t)\Psi(t)dt</math>
where
*ρ runs over the non-trivial zeros of the zeta function
*''p'' runs over positive primes
*''m'' runs over positive integers
*''F'' is a smooth function all of whose derivatives are rapidly decreasing
*ψ is a Fourier transform of ''F'': <math>\psi(t) = \int_{-\infty}^{\infty}F(x)e^{itx}dx</math>
*Φ(1/2 + it) = φ(t)
*Ψ(t) = -log(π) + Re(ψ(1/4 + it/2)), where ψ is the [[digamma function]] Γ′/Γ
==Hilbert-Pólya conjecture==
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