{"id":44,"date":"2018-01-08T16:37:00","date_gmt":"2018-01-08T16:37:00","guid":{"rendered":"https:\/\/math-sites.uncg.edu\/number-theory\/?p=44"},"modified":"2025-01-24T19:37:57","modified_gmt":"2025-01-24T19:37:57","slug":"hermite","status":"publish","type":"post","link":"https:\/\/math-sites.uncg.edu\/number-theory\/hermite\/","title":{"rendered":"Hermite Constants for Real Quadratic Fields"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-45 size-full\" src=\"https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/hermite_constant_disc.png\" alt=\"Hermite Constants for Real Quadratic Fields\" width=\"700\" height=\"400\" srcset=\"https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/hermite_constant_disc.png 700w, https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/hermite_constant_disc-300x171.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/p>\n<p>The Hermite constant for the ring of integers in real quadratic fields $$\\mathbb{Q}(\\sqrt{d})$$ for square-free positive integers $$d$$ are plotted above. The color of each point signifies the class number of the field. This is part of a current project of D. Yasaki into scaled trace forms over real quadratic fields.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Hermite constant for the ring of integers in real quadratic fields $$\\mathbb{Q}(\\sqrt{d})$$ for square-free positive integers $$d$$ are plotted above. The&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-44","post","type-post","status-publish","format-standard","hentry","category-number-theory"],"acf":[],"_links":{"self":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/44","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/comments?post=44"}],"version-history":[{"count":2,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/44\/revisions"}],"predecessor-version":[{"id":241,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/44\/revisions\/241"}],"wp:attachment":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/media?parent=44"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/categories?post=44"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/tags?post=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}