0
$\begingroup$

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.

Improve this question
$\endgroup$
3
  • $\begingroup$ Book by Harold Davenport "Multiplicative number theory" has a very nice exposition. $\endgroup$
    – Boris Bukh
    Commented Mar 14, 2012 at 10:31
  • 2
    $\begingroup$ 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. $\endgroup$
    – user9072
    Commented Mar 14, 2012 at 11:16
  • 2
    $\begingroup$ A proof that the density of primes congruent to $m$ (modulo some $N$ presumably) is $1/\phi(m)$ is unlikely to be found anywhere. $\endgroup$
    – Sean Eberhard
    Commented Mar 14, 2012 at 13:50

2 Answers 2

Reset to default
3
$\begingroup$

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

Improve this answer
$\endgroup$
1
$\begingroup$

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...

Improve this answer
$\endgroup$

Not the answer you're looking for? Browse other questions tagged .