Hypothesis
Version 2
Preserved in Portico This version is not peer-reviewed
On the Riemann Hypothesis for the Zeta Function
Version 1
: Received: 24 May 2021 / Approved: 25 May 2021 / Online: 25 May 2021 (14:44:37 CEST)
Version 2 : Received: 25 May 2021 / Approved: 26 May 2021 / Online: 26 May 2021 (11:44:31 CEST)
Version 3 : Received: 31 May 2021 / Approved: 1 June 2021 / Online: 1 June 2021 (07:58:45 CEST)
Version 2 : Received: 25 May 2021 / Approved: 26 May 2021 / Online: 26 May 2021 (11:44:31 CEST)
Version 3 : Received: 31 May 2021 / Approved: 1 June 2021 / Online: 1 June 2021 (07:58:45 CEST)
How to cite: Yang, X.-J. On the Riemann Hypothesis for the Zeta Function. Preprints 2021, 2021050616. https://doi.org/10.20944/preprints202105.0616.v2 Yang, X.-J. On the Riemann Hypothesis for the Zeta Function. Preprints 2021, 2021050616. https://doi.org/10.20944/preprints202105.0616.v2
Abstract
In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.
Keywords
Riemann zeta--function; entire Riemann zeta--function; completed Riemann zeta--function; Riemann $\Xi$--function; Riemann hypothesis
Subject
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.
Comments (1)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter: Xiao-Jun Yang
Commenter's Conflict of Interests: Author