Exact formulas for partial sums of the Möbius function expressed by partial sums weighted by the Liouville lambda function

Maxie Dion Schmidt

The Mertens function, $M(x):={\sum }_{n\le x}\mu (n)$, is defined as the summatory function of the classical Möbius function. The Dirichlet inverse function $g(n):=(\omega +1{)}^{-1}(n)$…