{"id":3416,"date":"2024-03-24T15:00:30","date_gmt":"2024-03-24T22:00:30","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3416"},"modified":"2024-03-25T18:59:54","modified_gmt":"2024-03-26T01:59:54","slug":"primitive-elements-in-number-fields-and-diophantine-avoidance-lenny-fukshansky-cmc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/primitive-elements-in-number-fields-and-diophantine-avoidance-lenny-fukshansky-cmc\/","title":{"rendered":"Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC)"},"content":{"rendered":"<p>The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K, called a primitive element. In fact, it is clear from the proof of this theorem that not only there are infinitely many such primitive elements in K, but in fact most elements in K are primitive. This observation raises the question about finding a primitive element of small &#8220;size&#8221;, where the standard way of measuring size is with the use of a height function. We discuss some conjectures and known results in this direction, as well as some of our recent work on a variation of this problem which includes some additional avoidance conditions. Joint work with Sehun Jeong (CGU).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K, called a primitive element. In fact, it is [&hellip;]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-3416","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K, called a primitive element. In fact, it is [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&amp;p=3416\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-26T01:59:54+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416\",\"name\":\"Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2024-03-24T22:00:30+00:00\",\"dateModified\":\"2024-03-26T01:59:54+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/colleges.claremont.edu\/ccms\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Events\",\"item\":\"https:\/\/colleges.claremont.edu\/ccms\/events\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/\",\"name\":\"Claremont Center for the Mathematical Sciences\",\"description\":\"Proudly Serving the Math Community at the Claremont Colleges Since 2007\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/colleges.claremont.edu\/ccms\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3416","og_locale":"en_US","og_type":"article","og_title":"Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences","og_description":"The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K, called a primitive element. 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