Authors: Hassine Saidane
Abstract. Based on the observation that several physical, biological and social processes seem to be optimizing an objective function such as an action or a utility, the Central Principle of Science was deemed to be Optimization. Indeed, optimization proved to be an efficient tool for uncovering several scientific laws and proving some scientific theories. In this paper, we use this paradigm to identify the location of the nontrivial zeros of the Riemann Zeta function (RZF). This approach enabled the formulation of this problem as a constrained optimization problem where a simple objective function referred to here as the “Push-Pull Action” is maximized. The solution of the resulting constrained nonlinear optimization problem proved that nontrivial zeros of RZF are located on the critical line. In addition to proving the Riemann Hypothesis, this approach unveiled a plausible law of “Maximum Action of Push-Pull” that seems to be driving RZF to its equilibrium states at the different heights where it reaches its nontrivial zeros. We also show that this law applies to functions exhibiting the same properties as RZF. Keywords: Zeta function, Riemann Hypothesis, Constrained Optimization
Comments: 8 Pages.
Unique-IP document downloads: 67 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.