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→Explicit formula for the Riemann zeta function: maybe this will improve legibility |
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:: <math>\varphi(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.
Roughly speaking, the explicit formula says the Fourier transform of the zeros of the zeta function is the set of prime powers plus some elementary factors.
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