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Computing the Mertens function on a GPU
Published 31 Jul 2011 in math.NT | (1108.0135v1)
Abstract: 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 ($M(x) \approx -1.996 \ast 109$ 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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