Riemann's hypothesis via Robin's Theorem

As essential condition for the validy of Robin’s Theorem as a precondition for the proof of the Riemann hypothesis, we show that the minimum of the function $F={\mathrm{e}}^{\gamma }\ln (\ln n)-\sigma (n)\mathrm{/}n$ is found to be positive. Therefore, $F>0$ holds for any $n>5040$.