Computing the Mertens function on a GPU
arXiv:1108.0135v1 [math.NT] (31 Jul 2011)
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 $exp{(10^{15})}$.
August 2, 2011 by hgpu
