{"title":"The least prime number represented by a binary quadratic form","authors":"Naser Talebizadeh Sardari","doi":"10.4171/jems/1031","DOIUrl":null,"url":null,"abstract":"Let $D 0$ is an absolute positive constant independent of $D$. More generally, let $K$ be a bounded degree number field over $\\mathbb{Q}$ with the discriminant $D_K$ and the class number $h_K.$ We conjecture that a positive proportion of the ideal classes of $K$ contain a prime ideal with a norm less than $h_K\\log(|D_K|)$.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2020-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1031","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 6
Abstract
Let $D 0$ is an absolute positive constant independent of $D$. More generally, let $K$ be a bounded degree number field over $\mathbb{Q}$ with the discriminant $D_K$ and the class number $h_K.$ We conjecture that a positive proportion of the ideal classes of $K$ contain a prime ideal with a norm less than $h_K\log(|D_K|)$.