Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Proof of the Riemann Hypothesis Based on Hadamard Product

Version 1 : Received: 4 August 2020 / Approved: 6 August 2020 / Online: 6 August 2020 (10:38:36 CEST)
Version 2 : Received: 25 September 2020 / Approved: 28 September 2020 / Online: 28 September 2020 (10:41:51 CEST)
Version 3 : Received: 3 March 2021 / Approved: 4 March 2021 / Online: 4 March 2021 (09:55:18 CET)

How to cite: Alhargan, F. A Proof of the Riemann Hypothesis Based on Hadamard Product. Preprints 2020, 2020080156. https://doi.org/10.20944/preprints202008.0156.v1 Alhargan, F. A Proof of the Riemann Hypothesis Based on Hadamard Product. Preprints 2020, 2020080156. https://doi.org/10.20944/preprints202008.0156.v1

Abstract

By unraveling a persistent misconception in the zeta Hadamard product expansion, and employing the zeta functional equation, a concise proof of the Riemann Hypothesis is presented, which conclusively demonstrate that the Riemann Hypothesis is true.

Keywords

the Riemann Hypothesis; the functional equation; the Riemann zeta function; Hadamard Product

Subject

Computer Science and Mathematics, Mathematics

Comments (0)

Comment 1
Received: 16 January 2021
Commenter: Joel Sjögren
The commenter has declared there is no conflict of interests.
Comment: Hello, equation (21) is true, but it does not follow from it alone that sigmar = 1/2. The equation is true of any set of numbers that is symmetric around both the real axis and the line re=1/2 and does not contain 0. For instance {i, -i, 1+i, 1-i} is such a set.
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