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

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.

• Autores: Mahecha Gómez, Jorge Eduardo; Castro Perelman, Carlos
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2002
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/39812
• Acceso en línea: https://hdl.handle.net/10495/39812
• Palabra clave: Riemann hypothesis; Index theory (Mathematics); Spectral theory (Mathematics); Heurística; Heuristics; Fractales; Fractals; Espacio y tiempo; Space and time; http://id.loc.gov/authorities/subjects/sh2005000907; http://id.loc.gov/authorities/subjects/sh85064861; http://id.loc.gov/authorities/subjects/sh85126408; https://id.nlm.nih.gov/mesh/D000066506
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-nd/2.5/co/