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