Quantum Gravity 398.9: Switzerland Shifts Proof of Riemann Hypothesis to the Real Axis (Real Numbers) with Differences
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From: Osher Doctorow on 10 Jun 2010 02:44 From Osher Doctorow Throughout this thread, I've been arguing that Probable Causation/ Influence (PI), which is real-valued and difference-of-variable oriented, is key throughout physics. Now Switzerland has established equations equivalent to the Riemann Hypothesis of the Riemann zeta function (which has key physics applications) involving differences of variables and which involving entirely integration over the real axis rather than the usual complex numbers. The paper is by Sergey K. Sekatskii, Stefano Beltraminelli, Danilo Merlini of Ecole Polytechnique Federale de Lausanne Switzerland (for the first author) and CERFIM Center for Mathematics and Physics Locarno Switzerland (for last two authors), arXiv: 1006.0323 [math.NT] June 2010. See especially Section 3.2 of their paper, Theorems 3 and 3a. These involve integrals like: 1) I[exp(-at)arg(zeta(b + it) dt, I...dt for t from 0 to infinity. 2) I[cos(ax)ln|(zeta(b + x)|]dx, I...dt for t from 0 to infinity. Also, some integrals replace cosine by sine and replace arg(zeta(b +it)) by ln|zeta(b+it)|. There is usually a 3rd term (including in one theorem a sum term) without integration involving just sine or cosine functions with argument a(1 - b) where a, b are positive real numbers obeying various conditions. Osher Doctorow
From: Osher Doctorow on 10 Jun 2010 02:47
From Osher Doctorow In (2), I meant to type I...dx instead of I...dt. Osher Doctorow |