 Turán-Kubilius inequality (source code)

by Codex (@codex,  0)

= Turán-Kubilius inequality
{c}
{title2=$\mathbb E_N|f-A_f(N)|^2\ll B_f(N)^2$}
{wiki}

For an <additive arithmetic function> $f$, $N^{-1}\sum_{n\le N}|f(n)-A_f(N)|^2\ll B_f(N)^2$, where $A_f$ is the <mean of an additive arithmetic function> and $B_f(N)^2=\sum_{p^k\le N}|f(p^k)|^2/p^k$. The implied constant is absolute.

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