Tuesday, June 18, 2013

1306.3711 (Stefano Beltraminelli et al.)

Riemann Hypozhesis: Architecture of a conjecture "along" the lines of
Pólya. From trivial zeros and Harmonic Oscillator to information about
non-trivial zeros of the Riemann zeta-function

Stefano Beltraminelli, Danilo Merlini, Sergey Sekatskii
We propose an architecture of a conjecture concerning the Riemann Hypothesis in the form of an "alternative" to the P\'olya strategy: we construct a Hamiltonian H_Polya whose spectrum coincides exactly with that of the Harmonic Oscillator Hamiltonian H_osc if and only if the Riemann Hypothesis holds true. In other words, it can be said that we formulate the Riemann Hypothesis by means of a non-commutative structure on the real axis, viz., that of the Harmonic Oscillator, by an equation of the type H_Polya(H_osc) = H_osc: the Harmonic Oscillator operator, if viewed as an argument of H_Polya, reproduces itself.
View original: http://arxiv.org/abs/1306.3711

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