Preprint Hypothesis Version 1 Preserved in Portico This version is not peer-reviewed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)

How to cite: Yang, X. On the Riemann hypothesis for the zeta function. Preprints 2021, 2021050616 (doi: 10.20944/preprints202105.0616.v1). Yang, X. On the Riemann hypothesis for the zeta function. Preprints 2021, 2021050616 (doi: 10.20944/preprints202105.0616.v1).

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.

Subject Areas

Riemann zeta--function, entire Riemann zeta--function, completed Riemann zeta--function, Riemann $\Xi$--function, Riemann hypothesis

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