This is based on well known
statistics used in signal processing called Rice Distributions (or Rayleigh-Rice)
that describe the distributions of Signal + Noise. (By signal, we
mean containing coherent phase structure). The Rice distribution was developed for
sonar and radar immediately after The Second World War (named after S. O. Rice,
who worked at Bell Labs) and there exists an extensive body of literature on
this subject.

The RICE distributions contain
a Modified I0 Bessel functions (of the 1st kind – zeroth
order) multiplied by the Rayleigh density, and my modification will be extended
to be RICE distribution multiplied by a combinatorial sum which will be a sum of
all possible signals. (This is appropriately normalised against the mean
level spacing

Of course, some mathematicians may not appreciate this in terms of proof and the approach has come from a seemingly unrelated area, but I believe these observations are of such interest that they demand explanation and investigation and the observations made cannot simply be dismissed. This note is therefore purely for discussion purposes only, and so does not constitute a formal research paper at this stage but expresses my thoughts.

Some features of various graphs and observations from all kinds of sources made with regard to the properties of the Zeta function can give us clues as to its form. This is the eclectic approach I have taken to weave together a consistent physical argument.

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