Functions and Analysis


The Optimization Principle for the Riemann Hypothesis

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.

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Submission history

[v1] 2018-06-28 10:42:13
[v2] 2018-07-01 07:28:05

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