Mathematics and Statistics Vol. 9(2), pp. 159 - 165
DOI: 10.13189/ms.2021.090210
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Some Remarks and Propositions on Riemann Hypothesis

Jamal Salah ^*
Department of Basic Science, College of Health and Applied Sciences, A’Sharqiyah University, Ibra post code 400, Oman

ABSTRACT

In 1859, Bernhard Riemann, a German mathematician, published a paper to the Berlin Academy that would change mathematics forever. The mystery of prime numbers was the focus. At the core of the presentation was indeed a concept that had not yet been proven by Riemann, one that to this day baffles mathematicians. The way we do business could have been changed if the Riemann hypothesis holds true, which is because prime numbers are the key element for banking and e-commerce security. It will also have a significant influence, impacting quantum mechanics, chaos theory, and the future of computation, on the cutting edge of science. In this article, we look at some well-known results of Riemann Zeta function in a different light. We explore the proofs of Zeta integral Representation, Analytic continuity and the first functional equation. Initially, we observe omitting a logical undefined term in the integral representation of Zeta function by the means of Gamma function. For that we propound some modifications in order to reasonably justify the location of the non-trivial zeros on the critical line: s= 1/2 by assuming that ζ(s) and ζ(1-s) simultaneously equal zero. Consequently, we conditionally prove Riemann Hypothesis.

KEYWORDS
Riemann Hypothesis, Analytic Continuity, Functional Equation, Non-trivial Zeros

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Jamal Salah , "Some Remarks and Propositions on Riemann Hypothesis," Mathematics and Statistics, Vol. 9, No. 2, pp. 159 - 165, 2021. DOI: 10.13189/ms.2021.090210.

(b). APA Format:
Jamal Salah (2021). Some Remarks and Propositions on Riemann Hypothesis. Mathematics and Statistics, 9(2), 159 - 165. DOI: 10.13189/ms.2021.090210.