Hypothesis
Version 3
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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. On the Riemann Hypothesis for the Zeta Function. Preprints 2021, 2021050616. https://doi.org/10.20944/preprints202105.0616.v3 Yang, X. On the Riemann Hypothesis for the Zeta Function. Preprints 2021, 2021050616. https://doi.org/10.20944/preprints202105.0616.v3
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.
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Commenter: Xiao-Jun Yang
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