let be the fucntion
$$ M(x)= \sum_{n= -\infty}^{\infty} \delta (x- \gamma _{n}) $$
here the sum of deltas run over the imaginary par of the Riemann zeros my first question is this in the sense of distribution equal to
$$ M(x)= \delta (\zeta (1/2+it) $$ assuming all the imaginary parts are real so RH is true
also if an imaginary part would be complex so $$ \gamma _{p}=ia $$ is then true that
$$ \int_{-\infty}^{\infty}f(x)\delta (x-ia) =0 $$
so the integral $ \int_{-\infty}^{\infty}M(x)f(x) $ depends on if RH is true or not