Riemann hypothesis and Robin's Inequality Implications

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Is the following statement true:

Let $\Bbb{A}$ be the set of all Natural numbers n, greater than or equal to 5041, for which the inequality $\displaystyle \sigma(n)<e^{\gamma}n\log\log n$ is not true (does not hold).

$\Bbb{A}$ = $\{\}$ $\Longleftrightarrow $ For all $\displaystyle s ≠ -2n:\zeta(s)=0∧0<Re[s]<1=1/2$

Consequently, is the following wikipedia article making the same explicit statement?

Why or why not?

Referencing

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1 Answer

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I put a copy of Nicolas 1983 here

I put a copy of Robin 1984 here.

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