{"id":15042,"date":"2022-06-16T20:10:48","date_gmt":"2022-06-17T00:10:48","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=15042"},"modified":"2026-06-09T09:55:27","modified_gmt":"2026-06-09T13:55:27","slug":"tr-206-enumeration-problems-relating-to-dirichlets-theorem","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1992\/tr-206-enumeration-problems-relating-to-dirichlets-theorem\/","title":{"rendered":"TR-206: Enumeration Problems Relating to Dirichlet&#8217;s Theorem"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-206: Enumeration Problems Relating to Dirichlet&#8217;s Theorem\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1992\/\">Technical Report<\/a>&nbsp;<strong>TR-206<\/strong><br>April 1992<\/p>\n\n\n\n<h2 id=\"enumeration-problems-relating-to-dirichlets-theorem\" class=\"wp-block-heading\">Enumeration Problems Relating to Dirichlet\u2019s Theorem<\/h2>\n\n\n\n<p>Evangelos Kranakis &amp; Michel Pocchiola<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>We consider enumeration problems relating to Dirichlet\u2019s theorem on the probability that two integers, taken at random, are relatively prime. We study weighted versions of the asymptotic number of lattice points inside a. domain 6 which a.re visible from the origin. This leads to a. uniform approach in the study of the asymptotic behavior of several problems in combinatorial and computational geometry like, the number of lines traversing at lea.st k vertices of a. cube or simplex, as well as the number of incidencies between a. set of points and lines and the complexity of the edge visibility region.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-206.pdf\">TR-206.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-206April 1992 Enumeration Problems Relating to Dirichlet\u2019s Theorem Evangelos Kranakis &amp; Michel Pocchiola Abstract We consider enumeration problems relating to Dirichlet\u2019s theorem on the probability that two integers, taken at random, are relatively prime. We study weighted versions of the asymptotic number of lattice points inside a. domain 6 which a.re visible from [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11910,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-15042","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=15042"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15042\/revisions"}],"predecessor-version":[{"id":24506,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15042\/revisions\/24506"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11910"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=15042"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=15042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}