Subject: FW: Probability Abstracts 52
From: "Norio KONO" 
To: 
Date: Wed, 1 Sep 1999 09:39:01 +0900

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1324. A PROOF OF THE RIEMANN HYPOTHESIS

Andrzej Madrecki

The starting point for the proof is the consideration of the abstact Hodge
decompositions and measures of functors. Involving the technique of
Gaussian measures in Banach spaces (specially important is possibility of
using of Fernique theorem) we linearize Green's function \mid z \mid^{-2}
through the functional Laplace transform which is the key to the proof
of the Riemann Hypothesis. Next we explain how the above results imply the
first of the two main technical results of the proof : the so called
Casteulnovo-Weil-Serre type inequality on the strong positivity of the
trace associated with the Riemann zeta function. The abstract Hodge type
decomposition and measure of \mid z \mid^{-2} (z \in C^{*}) is next used
to prove the main result of the paper- so called Riemann hypothesis
functional eqquation (RHFE in short) of the form:

Im(\zeta^{*}(s)) = Im(s)(2Re(s)-1)Tr(M_{G}M_{s})   s\in C, 

which immediately implies the Riemann Hypothesis.

madrecki@im.pwr.wroc.pl

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