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1996 Computing the summation of the Möbius function
Marc Deléglise, Joöl Rivat
Experiment. Math. 5(4): 291-295 (1996).


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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Marc Deléglise. Joöl Rivat. "Computing the summation of the Möbius function." Experiment. Math. 5 (4) 291 - 295, 1996.


Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 1007.11083
MathSciNet: MR1437219

Primary: 11Y35

Rights: Copyright © 1996 A K Peters, Ltd.

Vol.5 • No. 4 • 1996
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