### Computing the summation of the Möbius function

Marc Deléglise and Joöl Rivat
Source: Experiment. Math. Volume 5, Issue 4 (1996), 291-295.

#### Abstract

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, $M(10^{16})=-3195437$.

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Primary Subjects: 11Y35
Full-text: Open access