MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question

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

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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

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...

share|cite|improve this answer

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

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.