Computing the Mertens function on a GPU
arXiv:1108.0135v1 [math.NT] (31 Jul 2011)
@article{2011arXiv1108.0135K,
author={Kuznetsov}, E.},
title={"{Computing the Mertens function on a GPU}"},
journal={ArXiv e-prints},
archivePrefix={"arXiv"},
eprint={1108.0135},
primaryClass={"math.NT"},
keywords={Mathematics – Number Theory},
year={2011},
month={jul},
adsurl={http://adsabs.harvard.edu/abs/2011arXiv1108.0135K},
adsnote={Provided by the SAO/NASA Astrophysics Data System}
}
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
