Hello,

when one plots the Mertens function, it really looks like a fractal. So does anyone know the (approximate) value of the Hausdorff dimension of the set $\{(x,y),y=M(x),x\in\mathbb{R}^+\}$? Moreover, would there be a link between this Hausdorff dimension and the asymptotic behavior of the Mertens function? Thank you in advance.