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

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

2001-07-31

arxiv.org/abs/hep-th/0107266v3

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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+i\lambda_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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