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<h1 align=center> Li's criterion
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 Xian-Jin Li [
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<a href="http://www.ams.org/msnmain?fn=130&s1=98d:11101&pg1=MR">MR 98d:11101</a>
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The Riemann Hypothesis is true if and only if $\lambda_n\ge 0$ 
for each $n=1,2,\dots$ where
$$\lambda_n =\sum_\rho (1-(1-1/rho)^n)$$
Another expression for $\lambda_n$ is given by 
$$\lambda_n=\frac{1}{(n-1)!}\frac{d^n}{ds^n}(s^{n-1}\log \xi(s))\vert_{s=1}$$
and
$$\xi(s)=\frac12s(s-1)\Gamma(s/2)\zeta(s)$$
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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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