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<h1 align=center> Hardy-Littlewood series
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Hardy and Littlewood (Acta Mathematica 41 (1918), 119 - 196) showed that the Riemann Hypothesis is equivalent to the estimate 
 $$\sum_{k=1}^\infty \frac{(-x)^k}{k!\zeta(2k+1)}\ll x^{-1/4}$$
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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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