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Riemannin hypoteesi

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<strong>Riemannin</strong> <strong>hypoteesi</strong> ja lukuteoria<br />

Vuoden 1859 artikkelissaan Riemann johti kaavat joilla<br />

voidaan laskea π(x):lle tarkka-arvo<br />

π(x) =<br />

∞�<br />

n=1<br />

µ(n)<br />

n J � n √ x �<br />

J(x) = Li(x) − �<br />

Li (x ρ ) − log 2 +<br />

ρ∈S<br />

� ∞<br />

Yllä oleva on riippumaton <strong>hypoteesi</strong>sta!<br />

dt<br />

t (t 2 − 1) log t<br />

�<br />

x<br />

��<br />

−0.694

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