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

*Sun, 7 Nov 1999 09:01:21 +0200*

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----- Original Message -----

From: Matti Pitkänen <matpitka@rock.helsinki.fi>

To: <stephenk1@home.com>

Sent: Sunday, November 07, 1999 7:50 AM

Subject: Re: Physics and prime numbers (!)

*>
*

*> ----- Original Message -----
*

*> From: Stephen Paul King <stephenk1@home.com>
*

*> To: Matti Pitkänen <matpitka@pcu.helsinki.fi>
*

*> Cc: <stephenk1@home.com>
*

*> Sent: Saturday, November 06, 1999 11:16 PM
*

*> Subject: Re: Physics and prime numbers (!)
*

*>
*

*>
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*> > Hi Matti,
*

*> >
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*> > Is the article that you saw?
*

*> >
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*> Yes. This article was the article that inspired me to learn about Riemann
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*> hypothesis.
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*> Some comments below.
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*>
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*> > Later,
*

Still a comment about primes. I realized that there is indeed rather precise

duality

between Berry's supersymmetric theory and arithmetic quantum field theory if

the hypothesis about rationality of p^(iy) holds true.

a) Basic requirement is that the diagonal time development operator U(t) is

complex rational

valued for the allowed durations of time evolution. This implies that time

development

operator makes sense also as p-adic number for p mod 4=3.

b) In Berry's theory allowed durations of time evolution are log(n), n

integer and energys

are given by E=y, 1/2+iy zero of Riemann zeta.

c) In arithemetic QFT allowed durations of time evolution are y, and

energies are log(n).

It would seems that these theories are duals of each other.

Best,

MP

b) y corresponds

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