Comments on the Riemann conjecture and index theory on Cantorian fractal space-time
Abstract
Description
An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal branes living in Cantorian-fractal space-time, how the required $negative$ traces associated with those derivative operators naturally agree with the zeta function evaluated at the spectral dimensions. The $ζ(0) = - 1/2$ plays a fundamental role. Final remarks on the recent developments in the proof of the Riemann conjecture are made.
Revised Latex file. 22 pages. Remarks on the recent developments in the proof of the Riemann conjecture are made. Plots were included
Revised Latex file. 22 pages. Remarks on the recent developments in the proof of the Riemann conjecture are made. Plots were included