I just read a paper related to the Robin Inequality, and the abstract read:
"Abstract. Let σ(n) denote the sum of divisors function. In this paper we give a simple proof of the Robin inequality (R): σ(n) < $e^γ$n log log n, for all positive integers n ≥ 5041. The Robin inequality (R) implies Riemann Hypothesis."
So I'm confused as to what the state of the claim is? I've seen that the Robin inequality is true if and only if the RH is true. And this paper is saying that they prove the inequality. Does this mean the RH is proven? I suppose I'm not too sure what is actually being claimed here. Although I have only just learned of it.