{"id":5813,"date":"2017-06-21T18:09:29","date_gmt":"2017-06-21T16:09:29","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/?p=5813"},"modified":"2017-06-21T18:09:29","modified_gmt":"2017-06-21T16:09:29","slug":"11-fakultetski-seminar-on-mordells-equation-i-integral-basis-and-monogenity-in-parametric-families-of-number-fields","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/znanost\/11-fakultetski-seminar-on-mordells-equation-i-integral-basis-and-monogenity-in-parametric-families-of-number-fields\/","title":{"rendered":"11. Fakultetski seminar: \u201cOn Mordell&#8217;s equation\u201d i \u201eIntegral basis and monogenity in parametric families of number fields\u201c"},"content":{"rendered":"<p>Pozivamo Vas na <strong>11. fakultetski seminar <\/strong><strong>u srijedu 28. lipnja 2017. u amfiteatru 3F-A-0-1 u 12 sati<\/strong>\u00a0na kojem \u0107e<\/p>\n<p style=\"text-align: center\"><strong>prof. dr.sc<\/strong>. \u00a0<strong>Istv\u00e1n Ga\u00e1l<\/strong>,<\/p>\n<p style=\"text-align: center\">Mathematical Institute, University of \u00a0Debrecen,<\/p>\n<p>odr\u017eati predavanje pod naslovom<\/p>\n<p style=\"text-align: center\">\u00a0<strong>\u201e<\/strong><strong>On Mordell&#8217;s equation<\/strong><strong>\u201d,<\/strong><strong>\u00a0<\/strong><\/p>\n<p>te<\/p>\n<p style=\"text-align: center\"><strong>mag.math. L\u00e1szl\u00f3 Remete<\/strong>,<\/p>\n<p style=\"text-align: center\">Mathematical Institute, University of\u00a0 Debrecen<\/p>\n<p>odr\u017eati predavanje pod naslovom<\/p>\n<p style=\"text-align: center\">\u00a0<strong>\u201e<\/strong><strong>Integral basis and monogenity in parametric families of number fields\u201c.<\/strong><strong>\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Sa\u017eetak predavanja \u201eOn Mordell&#8217;s equation\u201d: \u00a0<\/strong><\/p>\n<p>We survey the history of Mordell&#8217;s classical equation x^3+k=y^2. Recently M.E.Pohst, M.Pohst and I.Ga\u00e1l gave an improvement of Wildanger&#8217;s method which makes possible to solve the equation up to |k|&lt;10^15. We give some details of the new method and give interesting examples.<\/p>\n<p><strong>Sa\u017eetak predavanja \u201eIntegral basis and monogenity in parametric families of number fields\u201c: <\/strong><strong>\u00a0<\/strong><\/p>\n<p>We consider infinite parametric families of number fields, pure extensions and the family of simplest sextic number fields. We show that the structure of their integral bases is periodic and explicitly give the integral bases. Using the integral basis we explicitly construct factors of the corresponding index form. This leads to conditions on the monogenity of the fields.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Kratki \u017eivotopis &#8211; Istv\u00e1n Ga\u00e1l:<\/strong><\/p>\n<ul>\n<li>1979-84: studies in mathematics at University of Debrecen (formerly Lajos Kossuth University)<\/li>\n<li>from 1984: staff member at University of Debrecen, Mathematical Institute, Department of Algebra and Number Theory<\/li>\n<li>1991-93: Fellow of the Alexander von Humboldt Foundation (host: Michael Pohst, D\u00fcsseldorf)<\/li>\n<li>1993-2010: vice director at the institute, vice dean of the faculty,<\/li>\n<li>2010-15: vice rector of the university<\/li>\n<li>2005-2016 head of the department<\/li>\n<li>editor of Publicationes Mathematicae, Acta Mathematica Academiae Paedagogicae Ny\u00edregyhaziensis, JP Journal of Algebra and Number Theory, local editor of Zentralblatt f\u00fcr Mathematik;<\/li>\n<li>research topics: diophantine equations, Thue equation, monogenity of number fields, power integral bases infnite parametric families of number fields<\/li>\n<li>author of about 75 paper and a book on power integral basis<\/li>\n<\/ul>\n<p><strong>Kratki \u017eivotopis &#8211; L\u00e1szl\u00f3 Remete:<\/strong><\/p>\n<ul>\n<li>2012-17 mathematics BSc and Msc studies at University of Debrecen<\/li>\n<li>from 2017: PhD student<\/li>\n<li>research topics: diophantine equations, Thue equation, monogenity of number fields, power integral bases infnite parametric families of number fields<\/li>\n<li>author of 8 papers<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Pozivamo Vas na 11. fakultetski seminar u srijedu 28. lipnja 2017. u amfiteatru 3F-A-0-1 u 12 sati\u00a0na kojem \u0107e prof. dr.sc. \u00a0Istv\u00e1n Ga\u00e1l, Mathematical Institute, University of \u00a0Debrecen, odr\u017eati predavanje pod naslovom \u00a0\u201eOn Mordell&#8217;s equation\u201d,\u00a0 te mag.math. L\u00e1szl\u00f3 Remete, Mathematical Institute, University of\u00a0 Debrecen odr\u017eati predavanje pod naslovom \u00a0\u201eIntegral basis and monogenity in parametric families [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":5122,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[23,2,24],"tags":[],"poredak":[],"class_list":["post-5813","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fakultetski-seminari","category-novosti","category-obavijesti"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>11. 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L\u00e1szl\u00f3 Remete, Mathematical Institute, University of\u00a0 Debrecen odr\u017eati predavanje pod naslovom \u00a0\u201eIntegral basis and monogenity in parametric families [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.pmfst.unist.hr\/znanost\/11-fakultetski-seminar-on-mordells-equation-i-integral-basis-and-monogenity-in-parametric-families-of-number-fields\/\" \/>\n<meta property=\"og:site_name\" content=\"Znanstvena djelatnost, PMF Split\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/pmfst\/\" \/>\n<meta property=\"article:published_time\" content=\"2017-06-21T16:09:29+00:00\" \/>\n<meta name=\"author\" content=\"autor\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@PmfSplit\" \/>\n<meta name=\"twitter:site\" content=\"@PmfSplit\" \/>\n<meta name=\"twitter:label1\" content=\"Napisao\/la\" \/>\n\t<meta name=\"twitter:data1\" content=\"autor\" \/>\n\t<meta name=\"twitter:label2\" content=\"Procijenjeno vrijeme \u010ditanja\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.pmfst.unist.hr\/znanost\/11-fakultetski-seminar-on-mordells-equation-i-integral-basis-and-monogenity-in-parametric-families-of-number-fields\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.pmfst.unist.hr\/znanost\/11-fakultetski-seminar-on-mordells-equation-i-integral-basis-and-monogenity-in-parametric-families-of-number-fields\/\"},\"author\":{\"name\":\"autor\",\"@id\":\"https:\/\/www.pmfst.unist.hr\/znanost\/#\/schema\/person\/8c4957fe31fd46303be41a1bd068040a\"},\"headline\":\"11. 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