4976

Computing the Mertens function on a GPU

Eugene Kuznetsov
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}

}

Download Download (PDF)   View View   Source Source   

1668

views

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 $exp{(10^{15})}$.
No votes yet.
Please wait...

* * *

* * *

HGPU group © 2010-2024 hgpu.org

All rights belong to the respective authors

Contact us: