{"title":"没有小秩的普适二次型的数域在大多数度上都存在","authors":"Vítězslav Kala","doi":"10.1017/S0305004122000214","DOIUrl":null,"url":null,"abstract":"Abstract We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"16 1","pages":"225 - 231"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Number fields without universal quadratic forms of small rank exist in most degrees\",\"authors\":\"Vítězslav Kala\",\"doi\":\"10.1017/S0305004122000214\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.\",\"PeriodicalId\":18320,\"journal\":{\"name\":\"Mathematical Proceedings of the Cambridge Philosophical Society\",\"volume\":\"16 1\",\"pages\":\"225 - 231\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Cambridge Philosophical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/S0305004122000214\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Cambridge Philosophical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/S0305004122000214","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Number fields without universal quadratic forms of small rank exist in most degrees
Abstract We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.
期刊介绍:
Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.