1/F Noise, the Measurement of Time and Number Theory
MICHEL PLANAT
Laboratoire de Physique et Métrologie des Oscillateurs du CNRS,
32 Avenue de l'Observatoire,
25044 Besançon Cedex, France
Fluctuation and Noise Letters , vol 1, no 1, R65-R79 (2001)
Abstract
Time and frequency measurements of a high frequency oscillator
need the comparison to a reference oscillator: the physical units
of the measurement are the integers and the relevant approach
is analytical number theory. We show this in the context of
the moon-sun calendar discovered in ancient Greece and in
the context of a communication receiver. It is shown that the
resets in time measurements are governed by continued fraction
expansions and that their low frequency statistics connects
to prime number theory. A link between Riemann hypothesis and 1/F
noise arises in this context.
