On SUSY-QM, fractal strings and steps towards a proof of the Riemann hypothesis

2001/07/31 by Carlos Castro, Castro, Carlos, Alex Granik +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Mathematics (math.GM) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.GM #math.MP

paper · pdf · doi:10.48550/arxiv.hep-th/0107266

18 pages, 3 figures, Latex, corrected typos, two references added, minor changes

arxiv created 2001/09/25 · arxiv updated 2009/11/30

Abstract

We present, using spectral analysis, a possible way to prove the Riemann's hypothesis (RH) that the only zeroes of the Riemann zeta-function are of the form s=1/2+iλ_n. A supersymmetric quantum mechanical model is proposed as an alternative way to prove the Riemann's conjecture, inspired in the Hilbert-Polya proposal; it uses an inverse eigenvalue approach associated with a system of p-adic harmonic oscillators. An interpretation of the Riemann's fundamental relation Z(s) = Z(1-s) as a duality relation, from one fractal string L to another dual fractal string L' is proposed.

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