Generalization of Poisson summation

zetafunction

if we have the Poisson sum formula

[tex] \sum_{n=-\infty}^\infty f(n)=\sum_{k=-\infty}^\infty F(k)[/tex]

with F being the Fourier transform of f, my question is can this formula be generalized for sums over primes, and so on ? for example if p runs over primes

[tex] \sum_{p}f(p)=\sum_{p} F(p)[/tex]