{"id":28,"date":"2018-01-08T16:26:02","date_gmt":"2018-01-08T16:26:02","guid":{"rendered":"https:\/\/math-sites.uncg.edu\/number-theory\/?p=28"},"modified":"2025-01-24T19:37:57","modified_gmt":"2025-01-24T19:37:57","slug":"zero-free","status":"publish","type":"post","link":"https:\/\/math-sites.uncg.edu\/number-theory\/zero-free\/","title":{"rendered":"Zeros and Zero-Free Regions of $$\\zeta^{(38)}$$"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-29 size-full\" src=\"https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/zeta-zerofree-k38.png\" alt=\"Zeros and Zero-Free Regions of $$\\zeta^{(38)}$$\" width=\"800\" height=\"600\" srcset=\"https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/zeta-zerofree-k38.png 800w, https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/zeta-zerofree-k38-300x225.png 300w, https:\/\/math-sites.uncg.edu\/number-theory\/wp-content\/uploads\/sites\/6\/2018\/01\/zeta-zerofree-k38-768x576.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>The plot shows the distribution of the zeros of the 38th derivative of the Riemann zeta function on the complex plane with the zero free regions for $$\\zeta^{(38)}$$ as described in <a href=\"https:\/\/math-sites.uncg.edu\/sites\/pauli\/publications\/binder-pauli-saidak_new-zero-free-regions.pdf\"> New Zero-Free Regions for the Derivatives of the Riemann Zeta Function <\/a> by <a href=\"http:\/\/www.math.TU-Berlin.de\/%7Etbinder\">Thomas Binder<\/a>, <a href=\"https:\/\/math-sites.uncg.edu\/directory\/pauli\/\">Sebastian Pauli<\/a>, and <a href=\"https:\/\/math-sites.uncg.edu\/directory\/saidak\/\">Filip Saidak<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The plot shows the distribution of the zeros of the 38th derivative of the Riemann zeta function on the complex plane with&#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-28","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\/28","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=28"}],"version-history":[{"count":4,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":247,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/28\/revisions\/247"}],"wp:attachment":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/media?parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/categories?post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/tags?post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}