Published July 4, 2022 | Version v3
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Riemann's Hypothesis. It is true twice.

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I have no doubt that the Riemann hypothesis is true and I like to say that may be true twice.
The purpose of this revision [v02] is to correct the error present in version [v01].
I report the error, how I discovered it and how I have correct it.
The formulation (1 b), object of the correction, concerns negative prime numbers, maybe they are not useful but I think they can exist.
How the error occurred: I used the function sum(n=1, nf, expr) of PARI-GP with the intention of forcing it to perform the summation of negative (n), but I wrote sum(n=1, nf, -n^s).
 I should have written sum(n=1, nf, (-n)^s), this would have forced PARI-GP to change the sign of (n) before performing the exponentiation. ...

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Updated
2025-12-21