Number Theory


An Optimization Approach to the Riemann Hypothesis

Authors: Hassine Saidane

A great deal of research has been and still is being devoted to the zeros of the Riemann Zeta function (RZF) that are in the critical strip and known as the nontrivial zeros of RZF. The Riemann Hypothesis (RH) states that these zeros are all located on the critical line . Although a large number of nontrivial zeros have proved to be located on the critical line through numerical computation methods, starting with Riemann’s manual computation of the first few zero, no analytical proof or disproof of RH has been found since its conjecture by Riemann in 1859. In this paper, we implement a novel analytical approach to RH based on optimization. This analysis tool proved successful in deriving some important scientific theories and laws. Such a success prompted us to use this tool to analytically derive the location of RZF nontrivial zeros in order to either prove or disprove the Riemann Hypothesis. This was achieved by formulating and solving the appropriate location optimization problem.

Comments: 3 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
[v7] 2019-07-02 11:20:24

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