{"title":"丢番图近似和随机迭代中的原始素数","authors":"Ruofan Li","doi":"10.4064/aa230303-12-8","DOIUrl":null,"url":null,"abstract":"We show that, under some mild conditions, the orbit of an algebraic number under random iterations cannot approach another algebraic number very fast. As an application of this result, we prove that, in certain cases, all but finitely many terms in such a","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"84 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diophantine approximation and primitive prime divisors in random iterations\",\"authors\":\"Ruofan Li\",\"doi\":\"10.4064/aa230303-12-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that, under some mild conditions, the orbit of an algebraic number under random iterations cannot approach another algebraic number very fast. As an application of this result, we prove that, in certain cases, all but finitely many terms in such a\",\"PeriodicalId\":37888,\"journal\":{\"name\":\"Acta Arithmetica\",\"volume\":\"84 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/aa230303-12-8\",\"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":"Acta Arithmetica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/aa230303-12-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Diophantine approximation and primitive prime divisors in random iterations
We show that, under some mild conditions, the orbit of an algebraic number under random iterations cannot approach another algebraic number very fast. As an application of this result, we prove that, in certain cases, all but finitely many terms in such a
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