Centered moment comparison for additive arithmetic functions
= Centered moment comparison for additive arithmetic functions
If a <strongly additive arithmetic function> $g$ is supported on <primes> up to $y$, its $j$th uniform <central moment> differs from the independent <Bernoulli random variables> model with probabilities $1/p$ by $O(jy^j(\sum_{p\le y}|g(p)|)^j/N)$. Expansion of divisibility <indicator functions> reduces the comparison to $\lfloor N/d\rfloor/N=1/d+O(1/N)$.