Looking at @Lucia's answer to this question it appears $\sum_{n=1}^\infty \frac{\mu(n)}{n^s}$ converges for $\sigma > \frac{1}{2}$. Can someone point me to a proof or provide proof for this? If I misunderstood and if this is not true, is it known for what minimum value of $\sigma$ will it converge?

Thanks in advance!