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<h1 align=center> Equivalences involving the Farey series
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Equidistribution of Farey sequence: Let $r_v$ be the elements of the Farey sequence of order $N$, $v=1,2,\dots \Phi(N)$ where $\Phi(N)=\sum_{n=1}^N\phi(n)$.  Let $\delta_v=r_v-v/\Phi(N)$.  Then RH if and only if 
$$\sum_{v=1}^{\Phi(N)} \delta_v^2\ll N^{-1+\epsilon}.$$
Also, RH if and only if
$$\sum_{v=1}^{\Phi(N)} |\delta_v|\ll N^{1/2+\epsilon}.$$


Here is [\begin{rawhtml}<a href="http://www.math.jussieu.fr/~miw/telecom/biblio-Amoroso.html">a good bibliography</a>\end{rawhtml}] on this subject.

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Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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