4 problems

Let $M(x)=\sum_{n\leq x}\mu(n)$ denote the summatory Möbius function. Ng's large-deviation conjecture. There exists a constant $B>0$ such that … This conjecture concerns the precis…

Weak Mertens conjecture.

Let $\mu(n)$ be the Möbius function and define the Mertens function by … Let $\overline{\varliminf}$ denote the upper limit of the lower limit. Gonek's conjecture. There exists a n…

Let $\mu(k)$ be the Möbius function and let … be the Mertens function. Let $\mathcal{M}=\left(\mathcal{M}_n\right)_{n\in\mathbb{N}^*}$ be the sequence of symmetric square matrices…