Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Demichel

Expand Messages
  • Phil Carmody
    ... And one with access to some fairly impressive computational clusters. Phil
    Message 1 of 8 , Jan 2, 2011
    • 0 Attachment
      --- On Sun, 1/2/11, WarrenS <warren.wds@...> wrote:
      > Andrey Kulsha pointed out this 2005
      > paper/lecture by Patrick Demichel,
      > who I think is an amateur, but evidently a very good one:

      And one with access to some fairly impressive computational clusters.

      Phil
    • Andrey Kulsha
      ... There are also two new (very similar, huh) papers analyzing and improving these results: http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf
      Message 2 of 8 , Jan 2, 2011
      • 0 Attachment
        > and it later got improved and turned into a published paper:
        >
        > Yannick Saouter & Patrick Demichel:
        > A sharp region where pi(x)-li(x) is positive,
        > Mathematics of Computation 79 (2010) 2395-2405.
        > http://www.ams.org/journals/mcom/2010-79-272/S0025-5718-10-02351-3/home.html

        There are also two new (very similar, huh) papers analyzing and improving these results:
        http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf
        http://eprints.ma.man.ac.uk/1547/01/SZproject2010.pdf

        Best regards,

        Andrey

        [Non-text portions of this message have been removed]
      • Phil Carmody
        ... In 1914, numerical evidence proved that π(x)
        Message 3 of 8 , Jan 2, 2011
        • 0 Attachment
          --- On Sun, 1/2/11, Andrey Kulsha wrote:
          > There are also two new (very similar, huh)
          > papers analyzing and improving these results:
          > http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf

          "In 1914, numerical evidence proved that π(x) < li(x) for all x. "

          Ewww...

          Phil
        • Phil Carmody
          ... It gets worse. Looking at the start of Chapter 3, Numerical Results (i), we have the assertion: Now we know that (gonna simplify glyphs, sorry) e^(iwy)
          Message 4 of 8 , Jan 2, 2011
          • 0 Attachment
            --- On Sun, 1/2/11, Phil Carmody wrote:
            > --- On Sun, 1/2/11, Andrey Kulsha wrote:
            > > There are also two new (very similar, huh)
            > > papers analyzing and improving these results:
            > > http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf
            >
            > "In 1914, numerical evidence proved that π(x) < li(x)
            > for all x. "
            >
            > Ewww...

            It gets worse. Looking at the start of Chapter 3, Numerical Results (i), we have the assertion:

            Now we know that (gonna simplify glyphs, sorry)

            e^(iwy) e^(iwy) e^(-iwy)
            ------- = ------- + --------
            p B + iy B - iy

            where none of the terms are defined. It seems chapter 2 most recently defined p = B + iy.

            So his assertion seems to be that:

            e^(iwy) e^(iwy) e^(-iwy)
            ------- = ------- + --------
            B + iy B + iy B - iy

            Or:

            e^(-iwy)
            0 = --------
            B - iy

            Or are my eyes playing tricks with me?

            Phil
          • Andrey Kulsha
            ... I guess they mean the conjugated pair of zeta zeros. Best regards, Andrey
            Message 5 of 8 , Jan 2, 2011
            • 0 Attachment
              > It gets worse. Looking at the start of Chapter 3, Numerical Results (i),
              > we have the assertion:
              >
              > Now we know that (gonna simplify glyphs, sorry)
              >
              > e^(iwy) e^(iwy) e^(-iwy)
              > ------- = ------- + --------
              > p B + iy B - iy

              I guess they mean the conjugated pair of zeta zeros.

              Best regards,

              Andrey
            • Phil Carmody
              ... Maths by guesswork? What happened to rigour? Then again, seeing how long those two take to get from 24/8 to 3, I suspect that the papers will be closely
              Message 6 of 8 , Jan 2, 2011
              • 0 Attachment
                --- On Sun, 1/2/11, Andrey Kulsha wrote:
                > > e^(iwy)    e^(iwy)   e^(-iwy)
                > > ------- =  ------- + --------
                > >    p        B + iy    B - iy
                >
                >     I guess they mean the conjugated pair of zeta zeros.

                Maths by guesswork? What happened to rigour? Then again, seeing how long those two take to get from 24/8 to 3, I suspect that the papers will be closely associated with rigor mortis.

                Phil
              • Kermit Rose
                _ ... Shows that that dissertation did not have careful proofreading. http://primes.utm.edu/howmany.shtml However in 1914 Littlewood proved that pi(x)-Li(x)
                Message 7 of 8 , Jan 2, 2011
                • 0 Attachment
                  _
                  > 3d. Re: Demichel
                  > Posted by: "Phil Carmody" thefatphil@... thefatphil
                  > Date: Sun Jan 2, 2011 4:32 am ((PST))
                  >
                  > --- On Sun, 1/2/11, Andrey Kulsha wrote:
                  >> There are also two new (very similar, huh)
                  >> papers analyzing and improving these results:
                  >> http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf
                  >
                  > "In 1914, numerical evidence proved that π(x)< li(x) for all x. "
                  >
                  > Ewww...
                  >
                  > Phil
                  >

                  Shows that that dissertation did not have careful proofreading.

                  http://primes.utm.edu/howmany.shtml

                  However in 1914 Littlewood proved that pi(x)-Li(x) assumes both positive
                  and negative values infinitely often.

                  Kermit
                Your message has been successfully submitted and would be delivered to recipients shortly.