{"id":617,"date":"2025-09-04T08:55:12","date_gmt":"2025-09-04T07:55:12","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=617"},"modified":"2025-09-04T08:57:00","modified_gmt":"2025-09-04T07:57:00","slug":"construccio-de-funcions-l-p-adiques","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/construccio-de-funcions-l-p-adiques\/","title":{"rendered":"Construcci\u00f3 de funcions-L p-\u00e0diques"},"content":{"rendered":"\n<p>Considerem la funci\u00f3 zeta de Riemann, que es defineix com<br \/>\n\\(\\zeta(s)=\\sum_{n\\geq 1} n^{-s}\\) per \\(s&gt;1\\). Fixem tamb\u00e9 un primer p.<br \/>\nEl treball consistir\u00e0 en entendre qu\u00e8 vol dir que aquesta funci\u00f3 (que<br \/>\npren valors complexos, en general) es pugui &#8220;interpolar<br \/>\np-\u00e0dicament&#8221;. Aquest proc\u00e9s dona lloc a una &#8220;versi\u00f3 p-\u00e0dica&#8221;,<br \/>\nposem \\(\\zeta_p(s)\\), on ara tant la variable s com els valors que<br \/>\npr\u00e8n la funci\u00f3 s\u00f3n nombres p-\u00e0dics. De l&#8217;exist\u00e8ncia d&#8217;aquesta versi\u00f3<br \/>\np-\u00e0dica se&#8217;n poden extreure propietats importants de la funci\u00f3<br \/>\ncomplexa \\(\\zeta(s)\\) original.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Considerem la funci\u00f3 zeta de Riemann, que es defineix com \\(\\zeta(s)=\\sum_{n\\geq 1} n^{-s}\\) per \\(s&gt;1\\). Fixem tamb\u00e9 un primer p. El treball consistir\u00e0 en entendre qu\u00e8 vol dir que aquesta funci\u00f3 (que pren valors complexos, en general) es pugui &#8220;interpolar p-\u00e0dicament&#8221;. Aquest proc\u00e9s dona lloc a una &#8220;versi\u00f3 p-\u00e0dica&#8221;, posem \\(\\zeta_p(s)\\), on ara tant la [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[53],"class_list":["post-617","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-marc-masdeu"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/617","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/77"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=617"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/617\/revisions"}],"predecessor-version":[{"id":620,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/617\/revisions\/620"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}