Submitted:
25 May 2021
Posted:
26 May 2021
Read the latest preprint version here
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
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