This proof is awesome!!!

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

________________________________

From: djbroadhurst <

d.broadhurst@...>

To:

primenumbers@yahoogroups.com
Sent: Thursday, September 1, 2011 7:46:15 PM

Subject: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression

--- In

primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> 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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