The de Bruijn-Newman constant is nonnegative, as proved in this fresh new preprint by Rodgers and Tao. It is also conjectured, but not proven yet, that $M(x)=O(\sqrt{x})$ is false, in which case it is actually equivalent to $\Lambda<0$. Time will tell.

The de Bruijn-Newman constant is nonnegative, as proved in this brand new preprint by Rodgers and Tao. It is also conjectured, but not proven yet, that $M(x)=O(\sqrt{x})$ is false, in which case it is actually equivalent to $\Lambda<0$. Time will tell.