{"id":20,"date":"2018-08-15T16:19:46","date_gmt":"2018-08-15T16:19:46","guid":{"rendered":"https:\/\/leeuwebpages.wpengine.com\/rmoy\/?page_id=20"},"modified":"2025-03-20T14:48:10","modified_gmt":"2025-03-20T19:48:10","slug":"research","status":"publish","type":"page","link":"https:\/\/webpages.leeu.edu\/rmoy\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20\" class=\"elementor elementor-20\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2a57 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a57\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-187e\" data-id=\"187e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-30e2 elementor-widget elementor-widget-text-editor\" data-id=\"30e2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignright size-medium wp-image-26\" src=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/gamma2-300x259.jpg\" alt=\"\" width=\"300\" height=\"259\" srcset=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/gamma2-300x259.jpg 300w, https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/gamma2.jpg 517w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><span style=\"font-family: georgia, palatino, serif\">My research interests mostly lie in the area of algebraic number theory with particular interest in understanding and computing Hilbert modular forms. I also have interests in various areas of discrete mathematics.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-35256ad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"35256ad\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-320b780\" data-id=\"320b780\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2e794e7 elementor-widget elementor-widget-text-editor\" data-id=\"2e794e7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span style=\"font-family: georgia, palatino, serif\">Publications:<\/span><\/h2><div><span style=\"font-family: georgia, palatino, serif\">The papers below may be found on the\u00a0<a href=\"http:\/\/arxiv.org\/find\/math\/1\/au:+Moy_R\/0\/1\/0\/all\/0\/1\" target=\"_blank\" rel=\"noopener\">arXiv<\/a> or <a href=\"https:\/\/scholar.google.com\/citations?hl=en&amp;user=yZZneb4AAAAJ\">Google Scholar<\/a>.<\/span><\/div><div><ul><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/2306-01633\/\">Monodromy groups of dessins d&#8217;enfant on rational polygonal billiards surfaces<\/a> (with J. Schmurr and J. Varlack). Accepted in <em>Rocky Mountain Journal of Mathematics<\/em>.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\">Finite abelian groups with toroidal subgroup lattices. <em>Journal of Algebraic Combinatorics<\/em>. 61 (2025), no. 30.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/monodromy\/\">Monodromy groups of dessins d&#8217;enfant on rational triangular billiards surfaces<\/a>. (with M. Mabe, J. Schmurr, and J. Varlack)\u00a0<em>Involve <\/em>16 (2023), no. 1, 49\u201358.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/sqfreepoly_2\/\">The distance to a squarefree polynomial over \ud835\udd3d<sub>2<\/sub>[x]<\/a>. (with <a href=\"http:\/\/people.math.sc.edu\/filaseta\/\">M. Filaseta<\/a>) <em>Acta Arithmetica<\/em> 193 (2020), no. 4, 419\u2013427.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/dessins.pdf\">Shabat polynomials and monodromy groups of trees uniquely determined by their passport<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\">(with <a href=\"https:\/\/www.spelman.edu\/academics\/majors-and-programs\/mathematics\/faculty\/naiomi-cameron\">N. Cameron<\/a>, <a href=\"https:\/\/www.linkedin.com\/in\/marymariekemp\/\">M. Kemp<\/a>, S. Maslak, <a href=\"https:\/\/math.uconn.edu\/person\/gabrielle-melamed\/\">G. Melamed<\/a>, <a href=\"https:\/\/www.linkedin.com\/in\/jonathan-pham-481055117\/\">J. Pham<\/a>, and <a href=\"https:\/\/math.osu.edu\/people\/wei.973\">A. Wei<\/a>)\u00a0<i>Involve <\/i>12 (2019), no. 5, 791\u2013812.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a style=\"margin: 0px\" href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/oddcharacterspaper.pdf\">Stanley sequences with odd character<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\"><i>Journal of Combinatorics <\/i>9 (2018), no. 4, 599\u2013618.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/truncatedbinomialgaloisgroup.pdf\">On the Galois group over \u211a of a truncated binomial expansion<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\">(with <a href=\"http:\/\/people.math.sc.edu\/filaseta\/\">M. Filaseta<\/a>) <i>Colloquium Mathematicum <\/i>154 (2018), no. 2, 295\u2013308.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/characterofindependentstanleysequences.pdf\">Characters of independent Stanley sequences<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\">(with <a href=\"http:\/\/www.mit.edu\/~msawhney\/\">M. Sawhney<\/a> and D. Stoner)\u00a0<i>European Journal of Combinatorics<\/i>\u00a070 (2018), 354\u2013363.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/novelstructure.pdf\">Novel structures in Stanley sequences<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\">(with <a href=\"http:\/\/www.davidrolnick.com\/\">D. Rolnick<\/a>)\u00a0<i>Discrete Mathematics<\/i>\u00a0339 (2016), no. 2, 689\u2013698.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/noncm.pdf\">There exist non-CM Hilbert modular forms of partial weight 1<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\">(with\u00a0<a href=\"http:\/\/www.math.jhu.edu\/~jspecter\/\">J. Specter<\/a>)\u00a0<i>International Mathematics Research Notices<\/i>\u00a0(2015), no. 24, 13047\u201313061.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/congruences-ramanujan.pdf\">Congruences for Ramanujan&#8217;s \u0192 and \u03c9 functions via generalized Borcherds products<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\">(with\u00a0<a href=\"https:\/\/www.bucknell.edu\/fac-staff\/jennifer-berg\">J. Berg<\/a>,\u00a0<a href=\"http:\/\/homepages.math.uic.edu\/~acasti8\/\">A. Castillo<\/a>,\u00a0<a href=\"https:\/\/people.math.wisc.edu\/~grizzard\/\">R. Grizzard<\/a>,\u00a0<a href=\"https:\/\/sites.google.com\/site\/vitakala\/\">V. Kala<\/a>, and C. Wang)\u00a0<i>The Ramanujan Journal<\/i>\u00a035 (2014), no. 2, 327\u2013338.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/congruences-among-power-series.pdf\">Congruences among power series coefficients of modular forms<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\"><i>International Journal of Number Theory<\/i>\u00a09 (2013), no. 6, 1447\u20131474.<\/span><\/li><li><span style=\"font-family: georgia, palatino, serif\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/stanley-sequences.pdf\">On the growth of the counting function of Stanley sequences<\/a>.<\/span><br \/><span style=\"font-family: georgia, palatino, serif\"><i>Discrete Mathematics<\/i>\u00a0311 (2011), no. 7, 560\u2013562.<\/span><\/li><\/ul><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/webpages.leeu.edu\/rmoy\/files\/2018\/08\/gamma2-300x259.jpg\" alt=\"\" width=\"300\" height=\"259\">My research interests mostly lie in the area of algebraic number theory with particular interest in understanding and computing Hilbert modular forms. I also have interests in various areas of discrete mathematics.<\/p>\n<p class=\"excerpt-link\"><a href=\"https:\/\/webpages.leeu.edu\/rmoy\/research\/\">&sim;&nbsp;Continue Reading&nbsp;&sim;<\/a><\/p>\n","protected":false},"author":384,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-20","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/pages\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/users\/384"}],"replies":[{"embeddable":true,"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":0,"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"wp:attachment":[{"href":"https:\/\/webpages.leeu.edu\/rmoy\/wp-json\/wp\/v2\/media?parent=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}