{"id":447,"date":"2015-04-06T21:58:27","date_gmt":"2015-04-07T01:58:27","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/alexb\/?p=447"},"modified":"2026-03-19T08:12:40","modified_gmt":"2026-03-19T12:12:40","slug":"robert_vaughan_second_talk_4_7_15","status":"publish","type":"post","link":"https:\/\/people.clas.ufl.edu\/alexb\/2015\/04\/06\/robert_vaughan_second_talk_4_7_15\/","title":{"rendered":"Robert C. Vaughan"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h2 class=\"wp-block-heading\">Zeros of Dirichlet series<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">When\/Where:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">April 7, 2015, 1:55 \u2014 2:45pm at LIT 368.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Abstract:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">We are concerned here with Dirichlet series<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">\\(f(s) = 1 +sum_{n=2}^{infty} frac{c(n)}{n^s} \\)<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">which satisfy a function equation similar to that of the Riemann zeta function, typically of the form<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">\\(f(s) = 2^s q^{1\/2-s} pi^{s-1} Gamma(1-s) big(sintextstylefrac{pi}{2}(s+kappa)big) f(1-s), \\)<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">but for which the Riemann hypothesis is false. We establish a plethora of such functions and show that the zeros of such functions are ubiquitous in the complex plane.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":331,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"featured_post":"off","footnotes":"","_links_to":"","_links_to_target":""},"categories":[5],"tags":[],"class_list":["post-447","post","type-post","status-publish","format-standard","hentry","category-nts-posting"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts\/447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/users\/331"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/comments?post=447"}],"version-history":[{"count":3,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts\/447\/revisions"}],"predecessor-version":[{"id":1195,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts\/447\/revisions\/1195"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/media?parent=447"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/categories?post=447"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/tags?post=447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}