Is there formula for sum of the Möbius function,
$$M(x)=\sum_{n\leq x}\mu (n)?$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this communityIs there formula for sum of the Möbius function,
$$M(x)=\sum_{n\leq x}\mu (n)?$$
The summatory function of the Moebius $\mu$-function is called the Mertens function $M(x)$ (which has been denoted by $f(x)$ here). An analytic formula for $M(x)$ is not known, but there are formulas involving the non-trivial zeros of the Riemann $\zeta$-function (sometimes assuming RH), see for example here.