Number Theory


An Optimization Approach to the Riemann Hypothesis

Authors: Hassine Saidane

The optimization of theoretical concepts such as action or utility functions enabled the derivation of important theories and laws in some scientific fields such as physics and economics. These breakthroughs suggested that the problem of the location of the Riemann Zeta Function’s (RZF) nontrivial zeros can be similarly 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 Karush-Kuhn-Tucker optimality conditions associated with the formulated nonlinear program.

Comments: 5 Pages.

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Submission history

[v1] 2018-11-02 17:55:05
[v2] 2018-11-04 14:37:02
[v3] 2019-03-08 09:31:11
[v4] 2019-04-13 07:50:24
[v5] 2019-05-17 20:25:24
[v6] 2019-05-18 12:13:53

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