{"id":4976,"date":"2011-08-02T17:14:07","date_gmt":"2011-08-02T14:14:07","guid":{"rendered":"http:\/\/hgpu.org\/?p=4976"},"modified":"2011-08-02T17:14:07","modified_gmt":"2011-08-02T14:14:07","slug":"computing-the-mertens-function-on-a-gpu","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=4976","title":{"rendered":"Computing the Mertens function on a GPU"},"content":{"rendered":"<p>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 $exp{(10^{15})}$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>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 [&hellip;]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[157,3],"tags":[1796,1162,20,1090],"class_list":["post-4976","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-paper","tag-mathematics","tag-number-theory","tag-nvidia","tag-nvidia-geforce-gtx-560"],"views":2364,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/4976","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4976"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/4976\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}