An overview of the concept of phase-locking at the non linear, geometric and
quantum level is attempted, in relation to finite resolution measurements in a
communication receiver and its 1/f noise. Sine functions, automorphic functions
and cyclotomic arithmetic are respectively used as the relevant trigonometric
tools. The common point of the three topics is found to be the Mangoldt
function of prime number theory as the generator of low frequency noise in the
coupling coefficient, the scattering coefficient and in quantum critical
statistical states. Huyghens coupled pendulums, the Adler equation, the Arnold
map, continued fraction expansions, discrete Mobius transformations, Ford
circles, coherent and squeezed phase states, Ramanujan sums, the Riemann zeta
function and Bost and Connes KMS states are some but a few concepts which are
used synchronously in the paper.Comment: submitted to the journal: Fluctuation and Noise Letters, March 13,
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