Submitted:
31 May 2021
Posted:
01 June 2021
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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.
Keywords:
Riemann zeta--function
; entire Riemann zeta--function
; completed Riemann zeta--function
; Riemann \(\Xi\)--function
; Riemann hypothesis
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