{"id":118,"date":"2010-05-28T21:57:25","date_gmt":"2010-05-28T19:57:25","guid":{"rendered":"http:\/\/leotheodon.com\/V4\/?p=118"},"modified":"2019-01-29T22:45:47","modified_gmt":"2019-01-29T21:45:47","slug":"ter-2010-les-sommes-de-gauss","status":"publish","type":"post","link":"https:\/\/www.leotheodon.com\/V4\/2010\/05\/28\/ter-2010-les-sommes-de-gauss\/","title":{"rendered":"[Projet] TER 2010 &#8211; Les Sommes de Gauss"},"content":{"rendered":"\n<p>Apr\u00e8s le&nbsp;<a href=\"page.php?id=9\"><strong>TIPE<\/strong><\/a>, voil\u00e0 enfin le <strong>TER<\/strong>, le Travail Encadr\u00e9 de Recherche. Il s\u2019agit plus exactement de produire un m\u00e9moire, et de le pr\u00e9senter \u00e0 la fin de l\u2019ann\u00e9e, en bin\u00f4me, sur un sujet de notre choix, en adoptant une attitude de chercheur.<\/p>\n\n\n\n<p>Nos travaux ont donc port\u00e9 sur la th\u00e9orie des nombres, et plus exactement sur les sommes de Gauss. Ces sommes ont cela de remarquables, qu\u2019elles ressemblent fortement \u00e0 des s\u00e9ries de Fourier discr\u00e8tes, et que de sommes de nombres complexes, on parvient \u00e0 prouver des th\u00e9or\u00e8mes purement arithm\u00e9tiques.<\/p>\n\n\n\n<p>En effet, les sommes de Gauss peuvent fournir une preuve de la loi de r\u00e9ciprocit\u00e9 quadratique (\u00e9galit\u00e9 \u00e0 facteur pr\u00e8s de deux crit\u00e8res d\u2019Euler), mais offrent \u00e9galement des r\u00e9sultats sur les polyn\u00f4mes r\u00e9guliers constructibles, ou encore le nombre de solutions d\u2019\u00e9quations diophantiennes, et le th\u00e9or\u00e8me de Chevalley.<\/p>\n\n\n\n<p>Ces r\u00e9sultats, accompagn\u00e9s de leur preuves, sont d\u00e9taill\u00e9s dans le rapport, la pr\u00e9sentation n\u2019\u00e9tant propos\u00e9e qu\u2019\u00e0 titre indicatif, sont int\u00e9r\u00eat \u00e9tant fortement diminu\u00e9 une fois sortie de son contexte.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p><strong>Remarque <\/strong>(Janvier 2019) <strong>:<\/strong><\/p><p>On regrettera parfois quelques erreurs dans les formules (erreurs de transcription qui sont facilement rep\u00e9rables) et quelques tournures de phrases maladroites.<\/p><\/blockquote>\n\n\n\n<p><strong>T\u00e9l\u00e9charger :<\/strong><\/p>\n\n\n\n<div class=\"wp-block-file\"><a href=\"http:\/\/leotheodon.com\/V4\/wp-content\/uploads\/2019\/01\/LT_TER_sommes_de_gauss.pdf\">&#8211; Le rapport au format pdf : <\/a><a href=\"http:\/\/leotheodon.com\/V4\/wp-content\/uploads\/2019\/01\/LT_TER_sommes_de_gauss.pdf\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a href=\"http:\/\/leotheodon.com\/V4\/wp-content\/uploads\/2019\/01\/LT_TER_sommes_de_gauss_pr.pdf\">&#8211; La pr\u00e9sentation au format pdf : <\/a><a href=\"http:\/\/leotheodon.com\/V4\/wp-content\/uploads\/2019\/01\/LT_TER_sommes_de_gauss_pr.pdf\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Apr\u00e8s le TIPE, voil\u00e0 enfin le TER, le Travail Encadr\u00e9 de Recherche. Il s\u2019agit plus exactement de produire un m\u00e9moire, et de le pr\u00e9senter \u00e0 la fin de l\u2019ann\u00e9e&#8230;<\/p>\n","protected":false},"author":1,"featured_media":175,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rop_custom_images_group":[],"rop_custom_messages_group":[],"rop_publish_now":"initial","rop_publish_now_accounts":[],"rop_publish_now_history":[],"rop_publish_now_status":"pending","_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[3,5],"tags":[31,16,11,19,20,18],"class_list":["post-118","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-math","tag-gauss","tag-math","tag-rapport","tag-ter","tag-tipe","tag-tpe"],"_links":{"self":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts\/118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/comments?post=118"}],"version-history":[{"count":3,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts\/118\/revisions"}],"predecessor-version":[{"id":260,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts\/118\/revisions\/260"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/media\/175"}],"wp:attachment":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/media?parent=118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/categories?post=118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/tags?post=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}