The distribution of the summatory function of the Möbius function
The distribution of the summatory function of the Möbius function
The summatory function of the Möbius function is denoted M(x). In this article we deduce conditional results concerning M(x) assuming the Riemann hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. Assuming these conjectures, we show that M(x), when appropriately normalized, possesses …