{"id":393,"date":"2025-07-11T12:41:32","date_gmt":"2025-07-11T11:41:32","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=393"},"modified":"2025-09-04T10:56:57","modified_gmt":"2025-09-04T09:56:57","slug":"la-funcio-zeta-de-carlitz","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/la-funcio-zeta-de-carlitz\/","title":{"rendered":"La funci\u00f3 zeta de Carlitz"},"content":{"rendered":"<p>Considerem l&#8217;anell de polinomis a coeficients un cos finit \\(F_q\\)\u00a0 i considera la $$\\zeta(n)=\\sum_{a\\; monic}\\frac{1}{a^n}$$ Donem un sentit anal\u00edtic a l&#8217;expressi\u00f3 donant un valor. Estudiareu si aquests valors son algebraics o no, si es pot escriure un an\u00e0leg de funci\u00f3 zeta de Riemann, i que succeeix als negatius i amb l&#8217;equaci\u00f3 funcional. El treball ha de centrar-se en definir i treballar una modificaci\u00f3 de la funci\u00f3 zeta de Carlitz proposada pel professor Federico Pellarin (2010) i el valor d&#8217;aquesta funci\u00f3 en el 1, fent una introducci\u00f3 a la funci\u00f3 zeta de Carlitz i l&#8217;analogia amb la funci\u00f3 zeta de Riemann.<\/p>\n<p>O modificacions del treball respecte la funci\u00f3 zeta de Carlitz-Goss descrita anteriorment.<\/p>\n<p>Referencies:<\/p>\n<p>David Goss: Basic Structures of Function Field Arithmetic, Springer 1996.<\/p>\n<p>David Goss: The ongoing binomial revolution.<\/p>\n<p>David Goss:-phenomenology.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Considerem l&#8217;anell de polinomis a coeficients un cos finit \\(F_q\\)\u00a0 i considera la $$\\zeta(n)=\\sum_{a\\; monic}\\frac{1}{a^n}$$ Donem un sentit anal\u00edtic a l&#8217;expressi\u00f3 donant un valor. Estudiareu si aquests valors son algebraics o no, si es pot escriure un an\u00e0leg de funci\u00f3 zeta de Riemann, i que succeeix als negatius i amb l&#8217;equaci\u00f3 funcional. El treball ha [&hellip;]<\/p>\n","protected":false},"author":63,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,29],"tags":[43],"class_list":["post-393","post","type-post","status-publish","format-standard","hentry","category-algebra","category-analisi-matematica","tag-francesc-bars"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/393","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\/63"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=393"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/393\/revisions"}],"predecessor-version":[{"id":622,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/393\/revisions\/622"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=393"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=393"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}