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Comments on the Riemann conjecture and index theory on Cantorian fractal space-time

Carlos Castro·Jorge Mahecha
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Abstract

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.

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Carlos Castro, Jorge Mahecha. 2001-04-08. Comments on the Riemann conjecture and index theory on Cantorian fractal space-time. https://arxiv.org/abs/hep-th/0009014

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