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THE QUANTUM RIEMANN WAVE
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Journal Article
THE QUANTUM RIEMANN WAVE
2017
Overview
The aim of this work is to describe a new formula relating the nontrivial zeros of the Riemann Zeta function to the energy levels of the harmonic oscillator, which we call the \"Riemann wave,\" whose nodes are located at the height of the non-trivial zeros (on the Riemann Hypothesis, RH). We illustrate the formula by means of various Figures, and we present a calculation up to relatively \"high\" heights. Then, we propose formally an \"operator\" in agreement to the Polya's idea, which involves here the Lambert W function. We call it the \"Quantum Riemann Wave.\" Some approximations of the implicit equation for this operator, as well as a special interesting approximation (with the use of the Montgomery bound on the fluctuations S(t) and an additional factor), are also discussed and illustrated with some numerical experiments and Figures.
Publisher
Nova Science Publishers, Inc
