{"title":"整数向量的对偶系统(一般问题及其在正二次型几何中的应用)","authors":"S. S. Ryshkov, R. M. Èrdal","doi":"10.1070/SM1993V074N02ABEH003361","DOIUrl":null,"url":null,"abstract":"After giving a brief introduction to our new \"theory of dual systems of integer vectors\", we give the first applications to the theory of positive quadratic forms. We consider the question of enumerating the L-polytopes of lattices, paying particular attention to the case of five-dimensional lattices. The results reported in this paper were announced earlier by the authors in Doklady [1]; here we give the details.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"103 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"DUAL SYSTEMS OF INTEGER VECTORS (GENERAL QUESTIONS AND APPLICATIONS TO THE GEOMETRY OF POSITIVE QUADRATIC FORMS)\",\"authors\":\"S. S. Ryshkov, R. M. Èrdal\",\"doi\":\"10.1070/SM1993V074N02ABEH003361\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"After giving a brief introduction to our new \\\"theory of dual systems of integer vectors\\\", we give the first applications to the theory of positive quadratic forms. We consider the question of enumerating the L-polytopes of lattices, paying particular attention to the case of five-dimensional lattices. The results reported in this paper were announced earlier by the authors in Doklady [1]; here we give the details.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"103 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1993V074N02ABEH003361\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1993V074N02ABEH003361","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
DUAL SYSTEMS OF INTEGER VECTORS (GENERAL QUESTIONS AND APPLICATIONS TO THE GEOMETRY OF POSITIVE QUADRATIC FORMS)
After giving a brief introduction to our new "theory of dual systems of integer vectors", we give the first applications to the theory of positive quadratic forms. We consider the question of enumerating the L-polytopes of lattices, paying particular attention to the case of five-dimensional lattices. The results reported in this paper were announced earlier by the authors in Doklady [1]; here we give the details.
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