Experimental Mathematics

Computing the summation of the Möbius function

Marc Deléglise and Joöl Rivat

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

Article information

Source
Experiment. Math. Volume 5, Issue 4 (1996), 291-295.

Dates
First available in Project Euclid: 13 March 2003

Permanent link to this document
http://projecteuclid.org/euclid.em/1047565447

Mathematical Reviews number (MathSciNet)
MR1437219

Zentralblatt MATH identifier
1007.11083

Subjects
Primary: 11Y35: Analytic computations

Citation

Deléglise, Marc; Rivat, Joöl. Computing the summation of the Möbius function. Experiment. Math. 5 (1996), no. 4, 291--295. http://projecteuclid.org/euclid.em/1047565447.


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