Number Theory

    

A Proof of Riemann Hypothesis by Vector Properties of Riemann Zeta Function and Rubber Strip Model

Authors: Tae Beom Lee

The Riemann Hypothesis (RH) states that the non-trivial zeros of the Riemann Zeta Function (RZF) ζ(s) or the Dirichlet Eta Function(DEF) η(s) for a complex variable s = x + iy is of the form s = 0.5 + iy. In this thesis, we treat each term of the RZF as a vector. We showed some vector properties of the RZF by tracing term vectors. If there exist zeros whose real part is not 0.5, such as ζ(α + iβ) = ζ(1-α + iβ) = 0, the trajectory of ζ(α + iy) and ζ(1-α + iy) must intersect at the origin when y = β. To check if this can happen, we introduced the rubber strip model, and by using the Cauchy-Riemann differential equations, we induced a contradiction, ζ(s) = constant, which proves the RH. In appendices, we provided the source programs for visualizing vector traces of the RZF. We also suggested three other possible proofs of the RH for further studies.

Comments: 26 Pages. The revised version of the previous one, 'Two Proofs of Riemann Hypothesis by Vector Properties of Riemann Zeta Function'

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Submission history

[v1] 2022-02-25 19:16:08

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