23067Re: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression
- Sep 2, 2011This proof is awesome!!!
Way too complicated for what it applies, but way too rich for the limits it implies!
From: djbroadhurst <d.broadhurst@...>
Sent: Thursday, September 1, 2011 7:46:15 PM
Subject: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression
--- In firstname.lastname@example.org,
"djbroadhurst" <d.broadhurst@...> wrote:
> Dirichlet's proof is here:For a modern account, in English, see
where Pete Clark remarks:
"One of the amazing things about the proof of Dirichlet's theorem
is how modern it feels. It is literally amazing to compare the
scope of the proof to the arguments we used to prove some of the
other theorems in the course, which historically came much later.
Let us be honest that the proof of Dirichlet's theorem is of
a difficulty beyond that of anything else we have attempted in
I remark that Selberg's "elementary proof" is also rather
difficult. It is elementary only in the sense that
he does not use complex characters or infinite sums:
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