{"title":"积分格的新不变量","authors":"Ryota Hayasaka, T. Miezaki, M. Toki","doi":"10.4036/IIS.2019.R.02","DOIUrl":null,"url":null,"abstract":"Let $\\Lambda$ be any integral lattice in Euclidean space. It has been shown that for every integer $n>0$, there is a hypersphere that passes through exactly $n$ points of $\\Lambda$. Using this result, we introduce new lattice invariants and give some computational results related to two-dimensional Euclidean lattices of class number one.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New Invariants for Integral Lattices\",\"authors\":\"Ryota Hayasaka, T. Miezaki, M. Toki\",\"doi\":\"10.4036/IIS.2019.R.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $\\\\Lambda$ be any integral lattice in Euclidean space. It has been shown that for every integer $n>0$, there is a hypersphere that passes through exactly $n$ points of $\\\\Lambda$. Using this result, we introduce new lattice invariants and give some computational results related to two-dimensional Euclidean lattices of class number one.\",\"PeriodicalId\":91087,\"journal\":{\"name\":\"Interdisciplinary information sciences\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Interdisciplinary information sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4036/IIS.2019.R.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Interdisciplinary information sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4036/IIS.2019.R.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let $\Lambda$ be any integral lattice in Euclidean space. It has been shown that for every integer $n>0$, there is a hypersphere that passes through exactly $n$ points of $\Lambda$. Using this result, we introduce new lattice invariants and give some computational results related to two-dimensional Euclidean lattices of class number one.
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