On the Riemann Hypothesis for the Zeta Function

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This paper proves that all zeros of the Riemann $\Xi$-function are real, thus establishing the truth of the Riemann hypothesis and deriving its associated equivalence theorems.

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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.

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europepmc
last seen: 2026-05-19T01:45:01.086888+00:00
unpaywall
last seen: 2026-05-22T02:00:06.705733+00:00
License: CC-BY-4.0