{"title":"对奇怪的数字字段的介绍。","authors":"Guillermo Mantilla-Soler","doi":"10.5802/JTNB.1140","DOIUrl":null,"url":null,"abstract":"It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this paper we define a family of number fields, that contains among others all odd degree Galois tame number fields, for which the converse is true. In other words, for a number field K in such family we prove that the spinor class of the integral trace carries no more information about K than the discriminant and the signature do.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"An introduction to oddly tame number fields.\",\"authors\":\"Guillermo Mantilla-Soler\",\"doi\":\"10.5802/JTNB.1140\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this paper we define a family of number fields, that contains among others all odd degree Galois tame number fields, for which the converse is true. In other words, for a number field K in such family we prove that the spinor class of the integral trace carries no more information about K than the discriminant and the signature do.\",\"PeriodicalId\":48896,\"journal\":{\"name\":\"Journal De Theorie Des Nombres De Bordeaux\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-01-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal De Theorie Des Nombres De Bordeaux\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/JTNB.1140\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Theorie Des Nombres De Bordeaux","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/JTNB.1140","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this paper we define a family of number fields, that contains among others all odd degree Galois tame number fields, for which the converse is true. In other words, for a number field K in such family we prove that the spinor class of the integral trace carries no more information about K than the discriminant and the signature do.
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