Proving Riemann Hypothesis through the Derivative of Zeta Reflection

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Author(s)

Salah Ameer 1,*

1. Conestoga College, Kitchener, ON, Canada

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2021.04.03

Received: 29 Apr. 2021 / Revised: 3 May 2021 / Accepted: 28 May 2021 / Published: 8 Dec. 2021

Index Terms

Riemann Zeta Function

Abstract

A novel proof is presented in this work indicating that all non-trivial zeros of the zeta function has a real part equal to ½. As no proof has been validated yet, this work was successful in introducing a proof through the use of elementary calculus theorems. A second version of the proof was also shown where a more advanced series analysis (e.g. Fourier series) is used.

Cite This Paper

Salah Ameer," Proving Riemann Hypothesis through the Derivative of Zeta Reflection ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.7, No.4, pp. 27-31, 2021. DOI: 10.5815/ijmsc.2021.04.03

Reference

[1]E. Titchmarsh, The Theory of the Riemann Zeta Function. Oxford University Press, Second edition, 1986.

[2]E. Bombieri, Problems of the Millennium: The Riemann Hypothesis, http://claymath.org/prizeproblems/ riemann.htm.

[3]M. Wolf, Will a Physicist Prove the Riemann Hypothesis? Reports on Progress in Physics, vol. 83, no. 3, 2020, p. 036001, doi:10.1088/1361-6633/ab3de7

[4]D. Farmer, Jensen polynomials are not a viable route to proving the Riemann Hypothesis. arXiv preprint arXiv:2008.07206, (2020).

[5]R. Deloin, Proof of Riemann Hypothesis. Asian Research Journal of Mathematics, 9(1): 1-8, 2018; Article no.ARJOM.40341.

[6]F. Galetto, A New Proof of the Riemann Hypothesis, Research Trends on Mathematics and Statistics Vol. 3 (2019), pp 23 – 36.

[7]J. Salah, Two Conditional proofs of Riemann Hypothesis. International Journal of Sciences: Basic and Applied Research (IJSBAR). Vol. 49, Issue 1, pp 74 – 83, 2020.

[8]F. Alhargan, A Concise Proof Of The Riemann Hypothesis Based On Hadamard Product. https://hal.archives-ouvertes.fr/hal-01819208v4, (2021).

[9]D. Platt and T. Trudgian, The Riemann hypothesis is true up to 3.1012.arXiv:2004.09675, 2020.

[10]E. Carneiro, A survey on Beurling-Selberg majorants and some consequences of the Riemann hypothesis, Mat. Contemp. 40 (2011), 149–172.