2000/09/30 by Carlos Castro, Jorge Mahecha
Physics and Astronomy · #hep-th
published as Chaos Solitons Fractals 13 (2002) 1407 · Revised Latex file. 22 pages. Remarks on the recent developments in the proof of the Riemann conjecture are made. Plots were included
arxiv created 2001/04/08 · arxiv updated 2009/11/30
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.