Proof of a Dirichlet's theorem using the Riemann zeta function?

Question

Someone could tell me if there is a proof of the Dirichlet's theorem on arithmetic progressions stated below using only the Riemann zeta function $\zeta(s)=\sum_{n=1}^\infty 1/n^s,\;\mbox{Re}(s)>1$? Someone reference?

Dirichlet's Theorem For any two positive coprime integers $a$ and $d$, there are infinitely many primes of the form $a + nd$, where $n \in \mathbb{N}$.

Answer 1

Yes, there is, but it is quite technical (at least the one I know), and at the same time sooooo beautiful! I suggest you read the first 30-40 pages of Davenport's Multiplicative Number Theory. It illustrates the ideas of Dirichlet and if you go through the details, not only you will enjoy the proof, but learn a lot of ideas that emerged from number theory.

Hope that helps,