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Introduction

My own investigation has been to derive a physical mechanism that produces the characteristic statistics of the Riemann Zeta function, which no one appears to have done. They have evolved through discussion and argument with experts in this field including Professor Sir Michael Berry who has taken a great deal of trouble to look and sanitise my ideas up to a point where he fundamentally disagrees with my approach. From this point, these observations are a result of culmination of my ideas. I believe I have taken a very open view without becoming fixated in a particular mathematical theory or purely a non-physical mathematical world-view, nor trying to bias results or fit data from the start. My own limited knowledge of Riemann Hypothesis calls up facts from my background in sonar and signal processing that I know to be true.

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 which shall represent a local noise level along the Critical Line).

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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