{"id":655,"date":"2024-10-18T15:35:51","date_gmt":"2024-10-18T15:35:51","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=655"},"modified":"2025-03-11T18:50:19","modified_gmt":"2025-03-11T18:50:19","slug":"number-theory-seminar-october-18-2024","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2024\/10\/18\/number-theory-seminar-october-18-2024\/","title":{"rendered":"Number Theory Seminar: October 18, 2024"},"content":{"rendered":"<p><strong>Location:<\/strong> 12:10 p.m. in Stevenson Center, room 1310<\/p>\n<p><strong>Speaker:<\/strong>\u00a0Walter Bridges\u00a0(University of North Texas)<\/p>\n<p><strong>Title:<\/strong> Zero attractors and sign changes in partition polynomials<\/p>\n<p><strong>Abstract:<\/strong>\u00a0 I will discuss new methods in the asymptotic theory of integer partitions with applications to the following two problems. The first problem concerns secondary terms in asymptotic equidistribution.\u00a0For example, if $p(a,b,n)$ denotes the number of partitions of $n$ with parts congruent to $a$ modulo $b$, then it is easy to show that $p(a_1,b,n) \\sim p(a_2,b,n)$ as $n \\to \\infty$ for all $0\\leq a_1,a_2 &lt; b$.\u00a0 On the other hand, the difference $p(a_1,b,n)-p(a_2,b,n)$ oscillates as $n \\to \\infty$ for any $a_1 \\neq a_2$.\u00a0A new technique allows us to predict the oscillation for this and similar problems.<\/p>\n<p>The second problem concerns zero attractors for sequences of partition polynomials.\u00a0 If the coefficients of the polynomial $P_n(\\zeta)$ count the number of partitions of $n$ into $m$ parts, then R. Stanley asked to identify the zero attractor of the sequence $P_n(\\zeta)$ as $n \\to \\infty$ \u2013 that is, the set of limit points of the zero sets of the $P_n(\\zeta)$.\u00a0 It was shown by Boyer and Goh that the zero attractor of $P_n(\\zeta)$ is a \u201cPac-Man\u201d shaped curve in the unit disk.\u00a0 We prove a zero attractor for partition polynomials that count hook lengths; somewhat surprisingly, the zero attractor features isolated points.<\/p>\n<p>This is joint work\u00a0with W. Craig, A. Folsom, J. Franke, T. Garnowski, J. Males and L. Rolen.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Location: 12:10 p.m. in Stevenson Center, room 1310 Speaker:\u00a0Walter Bridges\u00a0(University of North Texas) Title: Zero attractors and sign changes in partition polynomials Abstract:\u00a0 I will discuss new methods in the asymptotic theory of integer partitions with applications to the following two problems. The first problem concerns secondary terms in asymptotic equidistribution.\u00a0For example, if $p(a,b,n)$ denotes&#8230;<\/p>\n","protected":false},"author":74,"featured_media":749,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[11],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/03\/number-theory.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/655"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/74"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=655"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/655\/revisions"}],"predecessor-version":[{"id":656,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/655\/revisions\/656"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/749"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}