## Computing the summation of the Möbius function.(English)Zbl 1007.11083

Summary: We describe an elementary method for computing isolated values of $M(x)=\sum_{n\leq x}\mu(n),$ where $$\mu$$ is the Möbius function. The complexity of the algorithm is $$O(x^{2/3} (\log\log x)^{1/3})$$ time and $$O(x^{1/3} (\log\log x)^{2/3})$$ space. Certain values of $$M(x)$$ for $$x$$ up to $$10^{16}$$ are listed: for instance, $$M(10^{16})= -3195437$$.

### MSC:

 11Y35 Analytic computations 11Y70 Values of arithmetic functions; tables

### Keywords:

Möbius function; complexity
Full Text:

### References:

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