The Riemann Hypothesis : The Vision and How We Proceed

Frantz Olivier

doi:https://doi.org/10.14445/22315373/IJMTT-V69I3P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 3 | Year 2023 | Article Id. IJMTT-V69I3P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I3P508

The Riemann Hypothesis : The Vision and How We Proceed

Frantz Olivier

Received	Revised	Accepted	Published
10 Feb 2023	09 Mar 2023	22 Mar 2023	31 Mar 2023

Citation :

Frantz Olivier, "The Riemann Hypothesis : The Vision and How We Proceed," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 3, pp. 58-72, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I3P508

Abstract

The work in this document advances concepts and procedures that bridge the gap between the prime enumeration and the zeta zero location in three main segments. The first segment is based on the Egyptian enumeration system which is used in this work to design the Construction and Detachment Principle, with the goal of establishing an extension field where the zeta zero location resides side-by-side with the integer under study. In the absence of a reliable formulae, a limit point can be established using a set of heuristics from the Golden Ratio and the Egyptian Continuous Fraction Algorithm. The latter formed the genus of a method that identified a unique zeta zero for a given x value. This is done in accordance with Dimension.al Analysis to test the validity of the zeta zero location distribution with respect to the prime distribution. The second segment establishes two formulas to test the relevancies of the zeta location with respect to the volume of the knapsack boxes containing prime numbers up to a given x value. This document also provides a method to test whether the formula produces an accurate counting of the prime for the given value of x by using the Taylor Approximation Polynomial at the slope point. This slope is the closest point to where the zeta zero resides. In the third segment of the work, the results will show the distribution of the zeta zero’s location and, in doing so, lessen the need of finding the largest gap between prime numbers. Finally, Complex analysis as well as modal logic are explored to establish the parameters of a dynamic algorithm for the general solution of the π(x) conjecture.

Keywords

Riemann Hypothesis, Fraction Algorithm, Prime enumeration, Zeta zero location.

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