# sum over primes and its powers

are there examples in number theory where the series

$$\sum_{p} \sum_{m=-\infty}^{\infty}f(p^{m})$$ or

$$\sum_{m=-\infty}^{\infty}f(q^{m})$$ for fixed prime 'q' appear ??

i believe they may be relate to p-adic integrals $$\int_{Q_{p}}f(x)dx$$

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Could you add what $f$ and $Q_p$ are? – Nils Matthes Feb 6 '13 at 11:28
I'd guess that by $\int_{\mathbb{Q}_p}$ he means an integral over the $p$-adic numbers. – user54147 Feb 6 '13 at 11:32