# Dirichlet's theorem on prime density [closed]

Does anyone knows where I could find the proof of Dirichlet's theorem on the analytic density of primes congruent to a certain integer $m$, which turns out to be $\frac{1}{\varphi(m)}$?

Thanks a lot.

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## closed as too localized by quid, Chandan Singh Dalawat, GH from MO, Igor Rivin, Emil JeřábekMar 14 '12 at 12:29

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Book by Harold Davenport "Multiplicative number theory" has a very nice exposition. –  Boris Bukh Mar 14 '12 at 10:31
I voted to close this question. This is a very wellknown result and contained in plenty of textbooks and lecture notes on the subject. To just find some proof of it seems easy enough. –  quid Mar 14 '12 at 11:16
A proof that the density of primes congruent to $m$ (modulo some $N$ presumably) is $1/\phi(m)$ is unlikely to be found anywhere. –  Sean Eberhard Mar 14 '12 at 13:50

## 2 Answers

Serre's "Course in arithmetic" starts pretty low, and ends with that result. It is quite short too.

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Try 'Introduction to analytic number theory' by T.Apostol (Chapter 7)

Or the Selberg article "An elementary proof of Dirichlet's theorem about primes in an arithmetic progression"

There is also several course note available on the web, just search for "Introduction to analytic number theory" or "Dirichlet's theorem" on google...

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