{"id":238279,"date":"2018-11-06T17:19:56","date_gmt":"2018-11-07T01:19:56","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/generating-ray-class-fields-of-real-quadratic-fields-via-complex-equiangular-lines\/"},"modified":"2018-11-06T17:19:56","modified_gmt":"2018-11-07T01:19:56","slug":"generating-ray-class-fields-of-real-quadratic-fields-via-complex-equiangular-lines","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/generating-ray-class-fields-of-real-quadratic-fields-via-complex-equiangular-lines\/","title":{"rendered":"Generating ray class fields of real quadratic fields via complex equiangular lines"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Let K be a real quadratic field. For certain K with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of K using a numerical method that arose in the study of complete sets of equiangular lines in C<sup>d<\/sup> (known in quantum information as symmetric informationally complete measurements or sics). The construction in low dimensions suggests a general recipe for producing unit generators in infinite towers of ray class fields above arbitrary K and we summarise this in a conjecture. Such explicit generators are notoriously difficult to find, so this recipe may be of some interest. In a forthcoming paper we shall publish promising results of numerical comparisons between the logarithms of these canonical units and the values of L-functions associated to the extensions, following the programme laid out in the Stark Conjectures.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let K be a real quadratic field. For certain K with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of K using a numerical method that arose in the study of complete sets of equiangular lines in Cd (known in quantum information as symmetric informationally complete measurements or sics). The [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"arxiv","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2016-54","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Marcus Appleby, Steven Flammia, Gary 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