Pretentious distance
= Pretentious distance
{title2=$\mathbb D(f,g;x)$}
{wiki=Pretentious_number_theory}
For multiplicative functions bounded by one, the pretentious distance up to $x$ is defined by
$$
\mathbb D(f,g;x)^2
=\sum_{p\leq x}\frac{1-\Re(f(p)\overline{g(p)})}{p}.
$$
It measures how similarly $f$ and $g$ behave on primes.