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Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications

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Advances in Pure Mathematics 2021年第5期11卷 524-572页

作者： Prodromos Char. Papadopoulos Aristotle University National Hellenic Research Foundation Giannitsa (or Yiannitsa) Greece

In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions () which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.

关键词： Twin Problem Twin’s Problem unsolved mathematical problems Prime Number problems Millennium problems Riemann Hypothesis Riemann’s Hypothesis Number Theory Information Theory Probabilities Statistics Management Financial Applications Arithmetical Analysis Optimization Theory Stock Exchange Mathematics Approximation Methods Manifolds Economical Mathematics Random Variables Space of Events Strategy Games Probability Density Stock Market Technical Analysis Forecasting

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Clarifications for the Published Article: “A Solution to the Famous Twin’s Problem” in the APM of SCIRP at 24 September of 2019

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Advances in Pure Mathematics 2020年第9期10卷 547-587页

作者： Prodromos Char. Papadopoulos 1st Gymnasium in Giannitsa Giannitsa Greece

This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.

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