Number Theory

   

An Optimization Approach to the Riemann Hypothesis

Authors: Hassine Saidane

Abstract. Optimization of relevant concepts such as action or utility functions enabled the derivation of theories and laws in some scientific fields such as physics and economics. This fact suggested that the problem of the location of the Riemann Zeta Function’s (RZF) nontrivial zeros can be addressed in a mathematical programming framework. Using a constrained nonlinear optimization formulation of the problem, we prove that RZF’s nontrivial zeros are located on the critical line, thereby confirming the Riemann Hypothesis. This result is a direct implication of the Kuhn-Tucker necessary optimality conditions for the formulated nonlinear program. Keywords: Riemann Zeta function, Riemann Hypothesis, Optimization, Kuhn-Tucker conditions.

Comments: 4 Pages.

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Submission history

[v1] 2018-11-02 17:55:05
[v2] 2018-11-04 14:37:02

Unique-IP document downloads: 38 times

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