{"id":1684,"date":"2019-02-04T16:08:37","date_gmt":"2019-02-04T21:08:37","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=1684"},"modified":"2026-03-19T08:10:26","modified_gmt":"2026-03-19T12:10:26","slug":"jesse-thorner","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/jesse-thorner\/","title":{"rendered":"Jesse Thorner"},"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<h1 class=\"wp-block-heading\">Jesse Thorner<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">A new approach to bounding $L$-functions<\/h3>\n\n\n\n<p><br class=\"\">Abstract: \u00a0An $L$-function is a type of generating<br class=\"\">function with multiplicative structure which arises from either an<br class=\"\">arithmetic-geometric object (like a number field, elliptic curve,<br class=\"\">abelian variety) or an automorphic form. \u00a0The Riemann zeta function<br class=\"\">$\\zeta(s) = \\sum_{n=1}^{\\infty} n^{-s}$ is the prototypical example of<br class=\"\">an L-function. \u00a0While $L$-functions might appear to be an esoteric and<br class=\"\">special topic in number theory, time and again it has turned out that<br class=\"\">the crux of a problem lies in the theory of these functions. \u00a0Many<br class=\"\">equidistribution problems in number theory rely on one&#8217;s ability to<br class=\"\">accurately bound the size of $L$-functions; optimal bounds arise from<br class=\"\">the (unproven!) Riemann Hypothesis for $\\zeta(s)$ and its extensions<br class=\"\">to other $L$-functions. \u00a0I will discuss some motivating<br class=\"\">equidistribution problems along with recent work (joint with K.<br class=\"\">Soundararajan) which produces new bounds for $L$-functions by proving<br class=\"\">a suitable &#8220;statistical approximation&#8221; to the (extended) Riemann<br class=\"\">Hypothesis.<\/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":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1684","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1684","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=1684"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1684\/revisions"}],"predecessor-version":[{"id":3936,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1684\/revisions\/3936"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=1684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}