{"title":"The least common multiple of a bivariate quadratic sequence","authors":"Noam Kimmel","doi":"10.4064/aa220719-9-7","DOIUrl":null,"url":null,"abstract":"Let $F\\in \\mathbb Z[x,y]$ be some polynomial of degree 2. We find the asymptotic behaviour of the least common multiple of the values of $F$ up to $N$. More precisely, we consider $\\psi_F(N) = \\log(\\text{LCM}_{0 \\lt F(x,y)\\leq N}\\lbrace F(x,y) \\rbrace)$ a","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"28 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Arithmetica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/aa220719-9-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $F\in \mathbb Z[x,y]$ be some polynomial of degree 2. We find the asymptotic behaviour of the least common multiple of the values of $F$ up to $N$. More precisely, we consider $\psi_F(N) = \log(\text{LCM}_{0 \lt F(x,y)\leq N}\lbrace F(x,y) \rbrace)$ a
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