**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Thu, 4 Nov 1999 09:11:05 +0200 (EET)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**WDEshleman@aol.com: "[time 974] Re: [time 970] LaTex version of my paper"**Previous message:**Stephen P. King: "[time 972] Re: [time 969] Sharpened form of Riemann hypothesis and TGD"**In reply to:**Matti Pitkanen: "[time 969] Sharpened form of Riemann hypothesis and TGD"

On Wed, 3 Nov 1999, Stephen P. King wrote:

*> Dear Matti,
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*>
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*> I am reading and thinking hard about the implications of this idea! I
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*> am very interested in the relationship that you see between
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*> supersymmetry and the algebraic identity. I have a couple of questions:
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*> 1) Are the p-adic number fields well-orderable, e.g. can we define a
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*> unique > or < relation between pairs of p-adic numbers within the p-adic
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*> number fields?
*

No. This is reflected as ultrametricity, which

corresponds mathematically to spin glass property and is one of the

strongest motovations for introducing p-adicization.

*> 2) Are the p-adic number fields themselves well-orderable?
*

You probable mean that one could say that there is ordering

with respect to p in some sense? One can say that the larger

the value of p is, the more refined the p-adic topology is.

Best,

MP

*> Later,
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*>
*

*> Stephen
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*>
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*>
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*> Matti Pitkanen wrote:
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*> >
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*> > Dear Stephen and all,
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*> >
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*> > I have worked with the sharpened form of Riemann hypothesis
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*> > stating that the phase factors p^(iy) are Pythagorean
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*> > (complex rational) phases for all primes p when y corresponds
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*> > to zero z=1/2+iy of Riemann zeta.
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*> >
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*> > The sharpened hypothesis allows various interpretations: for instance,
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*> > the matrix elements of the time development operator
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*> > U(t) for arithmetic quantum field theories are
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*> > Pythagorean phases when *time t is quantized* such
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*> > that z=1/2+it corresponds to zero of Riemann zeta!
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*> >
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*> > For these values of time time development operator
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*> > of arithmetic QFT would allow p-adicization by
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*> > phase preserving canonical identification.
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*> >
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*> > I attach the tex file.
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*> >
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*> > Best,
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*> > MP
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*> >
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*> > ------------------------------------------------------------------------
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*> > Name: sRiemann.tex
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*> > sRiemann.tex Type: IBM techexplorer TeX files (APPLICATION/x-tex)
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*> > Encoding: BASE64
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*>
*

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