{"title":"关于 p + 2 不再有两个素数除数的素数 p 的 αp^2 + β 的一元模分布问题","authors":"T. Todorova","doi":"10.55630/mem.2024.53.039-056","DOIUrl":null,"url":null,"abstract":"A classical problem in analytic number theory is to study the distribution of frac- tional part αp^k + β, k ≥ 1 modulo 1, where α is irrational and p runs over the set of primes. We consider the subsequence generated by the primes p such that p + 2 is an almost-prime (the existence of infinitely many such p is another topical result in prime number theory) and prove that its distribution has a similar property.","PeriodicalId":517751,"journal":{"name":"Mathematics and Education in Mathematics","volume":" 29","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors\",\"authors\":\"T. Todorova\",\"doi\":\"10.55630/mem.2024.53.039-056\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A classical problem in analytic number theory is to study the distribution of frac- tional part αp^k + β, k ≥ 1 modulo 1, where α is irrational and p runs over the set of primes. We consider the subsequence generated by the primes p such that p + 2 is an almost-prime (the existence of infinitely many such p is another topical result in prime number theory) and prove that its distribution has a similar property.\",\"PeriodicalId\":517751,\"journal\":{\"name\":\"Mathematics and Education in Mathematics\",\"volume\":\" 29\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics and Education in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55630/mem.2024.53.039-056\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Education in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55630/mem.2024.53.039-056","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
解析数论中的一个经典问题是研究αp^k + β, k ≥ 1 modulo 1 中α为无理数且 p 在素数集合中的分布。我们考虑由素数 p 生成的子序列，使得 p + 2 几乎是一个素数（存在无限多个这样的 p 是素数理论的另一个热门结果），并证明其分布具有类似的性质。
On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors
A classical problem in analytic number theory is to study the distribution of frac- tional part αp^k + β, k ≥ 1 modulo 1, where α is irrational and p runs over the set of primes. We consider the subsequence generated by the primes p such that p + 2 is an almost-prime (the existence of infinitely many such p is another topical result in prime number theory) and prove that its distribution has a similar property.
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