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Re: Infinite Primes in an Arithmethic Progression

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

      > Alas I cannot find the proof on-line

      Dirichlet's proof is here:

      http://tinyurl.com/3ef2l4o

      David
    • djbroadhurst
      ... 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
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        --- 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
      • Mathieu Therrien
        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
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          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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