Ondřej ChwiedziukCharles University, Matěj DoležálekCharles University, Simona HlavinkováCharles University, Emma PěchoučkováCharles University, Zdeněk PezlarCharles University, Om PrakashCharles University, Anna RůžičkováCharles University, Mikuláš ZindulkaCharles University
{"title":"No proper generalized quadratic forms are universal over quadratic fields","authors":"Ondřej ChwiedziukCharles University, Matěj DoležálekCharles University, Simona HlavinkováCharles University, Emma PěchoučkováCharles University, Zdeněk PezlarCharles University, Om PrakashCharles University, Anna RůžičkováCharles University, Mikuláš ZindulkaCharles University","doi":"arxiv-2409.07941","DOIUrl":null,"url":null,"abstract":"We consider generalized quadratic forms over real quadratic number fields and\nprove, under a natural positive-definiteness condition, that a generalized\nquadratic form can only be universal if it contains a quadratic subform that is\nuniversal. We also construct an example illustrating that the\npositive-definiteness condition is necessary.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07941","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider generalized quadratic forms over real quadratic number fields and
prove, under a natural positive-definiteness condition, that a generalized
quadratic form can only be universal if it contains a quadratic subform that is
universal. We also construct an example illustrating that the
positive-definiteness condition is necessary.
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