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

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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
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 :