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## Re: Infinite Primes in an Arithmethic Progression

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• ... Dirichlet s proof is here: http://tinyurl.com/3ef2l4o David
Message 1 of 4 , Sep 1, 2011
Bob Gilson <bobgillson@...> wrote:

> Alas I cannot find the proof on-line

Dirichlet's proof is here:

http://tinyurl.com/3ef2l4o

David
• ... For a modern account, in English, see http://www.math.uga.edu/~pete/4400DT.pdf where Pete Clark remarks: One of the amazing things about the proof of
Message 2 of 4 , Sep 1, 2011

> Dirichlet's proof is here:
> http://tinyurl.com/3ef2l4o

For a modern account, in English, see
http://www.math.uga.edu/~pete/4400DT.pdf
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
this course."

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:
http://www.jstor.org/pss/1969454

David
• This proof is awesome!!! Way too complicated for what it applies, but way too rich for the limits it implies! ________________________________ From:
Message 3 of 4 , Sep 2, 2011
This proof is awesome!!!

Way too complicated for what it applies, but way too rich for the limits it implies!

________________________________
Sent: Thursday, September 1, 2011 7:46:15 PM
Subject: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression

> Dirichlet's proof is here:
> http://tinyurl.com/3ef2l4o

For a modern account, in English, see
http://www.math.uga.edu/~pete/4400DT.pdf
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
this course."

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:
http://www.jstor.org/pss/1969454

David

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