Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields
We study ideal lattices in $\mathbb{R}^2$ coming from real quadratic fields, and give an explicit method for computing all well-rounded twists of any such ideal lattice. We apply this to ideal lattices coming from Markoff numbers to construct infinite families of non-equivalent planar lattices with...
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creator | Damir, Mohamed Taoufiq Karpuk, David |
description | We study ideal lattices in $\mathbb{R}^2$ coming from real quadratic fields,
and give an explicit method for computing all well-rounded twists of any such
ideal lattice. We apply this to ideal lattices coming from Markoff numbers to
construct infinite families of non-equivalent planar lattices with good
sphere-packing radius and good minimum product distance. We also provide a
complete classification of all real quadratic fields such that the orthogonal
lattice is the only well-rounded twist of the lattice corresponding to the ring
of integers. |
doi_str_mv | 10.48550/arxiv.1806.04174 |
format | Article |
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and give an explicit method for computing all well-rounded twists of any such
ideal lattice. We apply this to ideal lattices coming from Markoff numbers to
construct infinite families of non-equivalent planar lattices with good
sphere-packing radius and good minimum product distance. We also provide a
complete classification of all real quadratic fields such that the orthogonal
lattice is the only well-rounded twist of the lattice corresponding to the ring
of integers.</description><identifier>DOI: 10.48550/arxiv.1806.04174</identifier><language>eng</language><subject>Mathematics - Number Theory</subject><creationdate>2018-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1806.04174$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1806.04174$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Damir, Mohamed Taoufiq</creatorcontrib><creatorcontrib>Karpuk, David</creatorcontrib><title>Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields</title><description>We study ideal lattices in $\mathbb{R}^2$ coming from real quadratic fields,
and give an explicit method for computing all well-rounded twists of any such
ideal lattice. We apply this to ideal lattices coming from Markoff numbers to
construct infinite families of non-equivalent planar lattices with good
sphere-packing radius and good minimum product distance. We also provide a
complete classification of all real quadratic fields such that the orthogonal
lattice is the only well-rounded twist of the lattice corresponding to the ring
of integers.</description><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz81KAzEUhuFsXEj1AlyZG5jxZHIyk9lVitXCgFgLXQ5nJicQSB1Jpv7cvba6-uBdfPAIcaOgRGsM3FH6Ch-lslCXgKrBS7Hcc4zFdjq-OXZy9xnynOXk5cYxRdnRPIeRs_RpOsjtKb0cySX6rXIdOLp8JS48xczX_7sQr-uH3eqp6J4fN6v7rqC6waLVQ-W9tgqQ9Nh4g0AaXNU2xgzGj-Rdi0wWjVJY14OGalTsGAZiZZVeiNu_17Ogf0_hQOm7P0n6s0T_AEwxQrU</recordid><startdate>20180611</startdate><enddate>20180611</enddate><creator>Damir, Mohamed Taoufiq</creator><creator>Karpuk, David</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180611</creationdate><title>Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields</title><author>Damir, Mohamed Taoufiq ; Karpuk, David</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-93b2ff38104a3c7f540a30d29755b5fcafd94ea84511466b302c1ede0bae1813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Damir, Mohamed Taoufiq</creatorcontrib><creatorcontrib>Karpuk, David</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Damir, Mohamed Taoufiq</au><au>Karpuk, David</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields</atitle><date>2018-06-11</date><risdate>2018</risdate><abstract>We study ideal lattices in $\mathbb{R}^2$ coming from real quadratic fields,
and give an explicit method for computing all well-rounded twists of any such
ideal lattice. We apply this to ideal lattices coming from Markoff numbers to
construct infinite families of non-equivalent planar lattices with good
sphere-packing radius and good minimum product distance. We also provide a
complete classification of all real quadratic fields such that the orthogonal
lattice is the only well-rounded twist of the lattice corresponding to the ring
of integers.</abstract><doi>10.48550/arxiv.1806.04174</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Number Theory |
title | Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields |
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