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<h1 align=center> Averages
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These equivalent statements have the following shape :
$$
\sum_{n \leq x} f(n) = F(x) + O(x^{\alpha + \epsilon}), \quad x \rightarrow +\infty,
$$
where $f$ is an arithmetic function, $F(x)$ a smooth approximation to $\sum_{n \leq x} f(n)$, and $\alpha$ a real number.\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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