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<h1 align=center> Amoroso's criterion
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Amoroso [
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<a href="http://www.ams.org/msnmain?fn=130&s1=98f:11113&pg1=MR">MR 98f:11113</a>
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$$\tilde h(F_N) = (2\pi)^{-1}\int_{-\pi}^\pi \log^+|F(e^{i\theta})|~d\theta.$$
Then,   $\tilde h(F_n) \ll N^{\lambda + \epsilon}$ is equivalent to the assertion that the Riemann zeta function does not vanish for ${\rm Re}{z} \ge \lambda + \epsilon$.\begin{rawhtml}
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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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