Version 1
: Received: 9 September 2023 / Approved: 12 September 2023 / Online: 12 September 2023 (08:55:16 CEST)
Version 2
: Received: 25 July 2024 / Approved: 26 July 2024 / Online: 26 July 2024 (13:01:23 CEST)
How to cite:
De, S. On Some Specific Order Estimates for the Mertens Function and Its Relation to the Non-trivial Zeros of $\zeta(s)$. Preprints2023, 2023090723. https://doi.org/10.20944/preprints202309.0723.v2
De, S. On Some Specific Order Estimates for the Mertens Function and Its Relation to the Non-trivial Zeros of $\zeta(s)$. Preprints 2023, 2023090723. https://doi.org/10.20944/preprints202309.0723.v2
De, S. On Some Specific Order Estimates for the Mertens Function and Its Relation to the Non-trivial Zeros of $\zeta(s)$. Preprints2023, 2023090723. https://doi.org/10.20944/preprints202309.0723.v2
APA Style
De, S. (2024). On Some Specific Order Estimates for the Mertens Function and Its Relation to the Non-trivial Zeros of $\zeta(s)$. Preprints. https://doi.org/10.20944/preprints202309.0723.v2
Chicago/Turabian Style
De, S. 2024 "On Some Specific Order Estimates for the Mertens Function and Its Relation to the Non-trivial Zeros of $\zeta(s)$" Preprints. https://doi.org/10.20944/preprints202309.0723.v2
Abstract
The primary purpose of this article is to provide a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$ and, to derive specific order estimates for $M(n)$, in order to analyze the location of the non-trivial zeros of the \textit{Riemann Zeta function} $\zeta(s)$. A priori using the above concepts, the article aims at establishing a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
