Computing the Mertens function on a GPU

Mathematics – Number Theory

Scientific paper

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Scientific paper

A GPU implementation of an algorithm to compute the Mertens function in
O(x2/3+{\ko}) time is discussed. Results for x up to $10^{22}$, and a new
extreme value for $M(x)/x^{1/2}$, -0.585768 ($M(x) \approx -1.996 \ast 10^9$ at
$x \approx 1.161 \ast 10^{19}$), are reported.An approximate algorithm is used
to examine values of M(x) for x up to $\exp{(10^{15})}$.

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