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My hypothesis/ conjecture where the primes meet chaos in Riemann's conjecture

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  • Roger Bagula
    I have been working in complex dynamics for years and have done recent work in minimal surfaces and constant mean curvature surfaces. It never occurred to me
    Message 1 of 1 , Sep 3, 2003
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      I have been working in complex dynamics for years and
      have done recent work in minimal surfaces
      and constant mean curvature surfaces.
      It never occurred to me to use that knowledge
      on the Zeta zeros connection to the distribution of the primes.
      The key seems to be something called the Gauss map:
      {x0,y0,z0}={ 2*Re[Zeta[z]]/(1+Abs[Zeta[z]]^2),
      2*Im[Zeta[z]]/(1+Abs[Zeta[z]]^2), (1-Abs[Zeta[z]]^2)/(1+Abs[Zeta[z]]^2)}
      where
      x0^2+y0^2+z0^2=1
      Suppose we have a nontrivial zeta zero:
      f[n]=Zeta[1/2+I*b[n]]=0
      Then we get for the Gauss Map:
      {x0,y0,z0}={ 2*Re[Zeta[1/2+I*b[n]]], 2*Im[Zeta[1/2+I*b[n]]], 1}
      This gives
      1+2*Re[Zeta[1/2+i*b[n]]]+I*2*Im[Zeta[1/2+i*b[n]]]=Exp[I*2*Pi*C[n]]
      My hypothesis/ conjecture is that in order for the result to be on a
      unit circle as the Gauss Map puts it:
      C[n]=Arg[1+2*Re[Zeta[1/2+I*b[n]]],2*Im[Zeta[1/2+I*b[n]]]]/(2*Pi)
      That
      C[n]=Mod[Prime[n]*Irr,1]
      That is for the primes to be connected to the distribution of the zeta zeros
      as Riemann thought, there must be some irrational number "Irr"
      that forms an irrational rotation that connects the Primes to the zeta
      zeros.
      Another way to put is is that
      when the 1/2+I*b[n] is projected
      onto a unit sphere in the Riemannian manner
      the result is a circle with points
      at the b[n] points that correspond to the irrational rotation
      determined by the primes themselves.
      The alternative to this conjecture is
      a sequence of irrational numbers with no determining
      equation. My quantum energy equation for the primes shows that there
      is an ordering principle involved.
      I further conjecture that "Irr" is an transcendental number
      and that Riemann's conjecture as a result can
      never be proved as it is a Turing problem with no stopping point/
      transfinite.
      So this idea gives an inverse problem between the primes and the Zeta
      zeros.
      And it isn't an easy one: either the constant "Irr" exists or there is a
      sequence,
      but in both cases it is still an inverse problem. And the problem still
      involves
      a circle and irrational numbers....

      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL : http://home.earthlink.net/~tftn
      URL : http://victorian.fortunecity.com/carmelita/435/
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