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Huyghens, Bohr, Riemann and Galois: Phase-Locking

Michel R. P. Planat
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Abstract

Several mathematical views of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory. Two types of quantum phase-locking operators are defined, one acting on the rational numbers, the other on the elements of a Galois field. In both cases we analyse in detail the phase properties and find them related respectively to the Riemann zeta function and to incomplete Gauss sums.

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Michel R. P. Planat. 2005-10-11. Huyghens, Bohr, Riemann and Galois: Phase-Locking. https://doi.org/10.1142/s0217979206034340

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