{"id":86,"date":"2008-07-27T16:17:43","date_gmt":"2008-07-27T15:17:43","guid":{"rendered":"https:\/\/wpethzprd.ethz.ch\/kowalski\/2008\/07\/27\/the-chebotarev-invariant-of-we_8\/"},"modified":"2024-02-20T13:40:58","modified_gmt":"2024-02-20T11:40:58","slug":"the-chebotarev-invariant-of-we_8","status":"publish","type":"post","link":"https:\/\/blogs.ethz.ch\/kowalski\/2008\/07\/27\/the-chebotarev-invariant-of-we_8\/","title":{"rendered":"The Chebotarev invariant of W(E_8)"},"content":{"rendered":"<p>A quick follow-up to the previous post: D. Zywina has found the value of the Chebotarev invariant for the Weyl group of <em><strong>E<\/strong><sub>8<\/sub><\/em>, which is<\/p>\n<p>$latex c(W(E_8))= 4.19424758989300188767793949869\\ldots$<\/p>\n<p>So you would typically expect to need to look at a bit more than four Frobenius conjugacy classe, on average, to check that a Galois extension with group a subgroup of <em>W(<strong>E<\/strong><sub>8<\/sub>) <\/em>is not smaller. As we managed to do it with only two with F. Jouve in our particular case, this means that we were indeed somewhat lucky.<\/p>\n<p>(Thanks to Nguyen Ngoc Dong Quan for also proposing to do the computation with Magma).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A quick follow-up to the previous post: D. Zywina has found the value of the Chebotarev invariant for the Weyl group of E8, which is $latex c(W(E_8))= 4.19424758989300188767793949869\\ldots$ So you would typically expect to need to look at a bit more than four Frobenius conjugacy classe, on average, to check that a Galois extension with &hellip; <a href=\"https:\/\/blogs.ethz.ch\/kowalski\/2008\/07\/27\/the-chebotarev-invariant-of-we_8\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">The Chebotarev invariant of W(E_8)<\/span><\/a><\/p>\n","protected":false},"author":625,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-86","post","type-post","status-publish","format-standard","hentry","category-blogroll"],"_links":{"self":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/86","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/users\/625"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/comments?post=86"}],"version-history":[{"count":0,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/86\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/media?parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/categories?post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/tags?post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}