{"title":"素数的显式区间估计","authors":"Michaela Cully-Hugill, Ethan S. Lee","doi":"10.1090/mcom/3719","DOIUrl":null,"url":null,"abstract":"Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of $(\\Delta, x_0)$ such that for all $x \\geq x_0$ there exists at least one prime in the interval $(x(1 - \\Delta^{-1}), x]$.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Explicit interval estimates for prime numbers\",\"authors\":\"Michaela Cully-Hugill, Ethan S. Lee\",\"doi\":\"10.1090/mcom/3719\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of $(\\\\Delta, x_0)$ such that for all $x \\\\geq x_0$ there exists at least one prime in the interval $(x(1 - \\\\Delta^{-1}), x]$.\",\"PeriodicalId\":18301,\"journal\":{\"name\":\"Math. Comput. Model.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Math. Comput. Model.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mcom/3719\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Math. Comput. Model.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mcom/3719","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of $(\Delta, x_0)$ such that for all $x \geq x_0$ there exists at least one prime in the interval $(x(1 - \Delta^{-1}), x]$.
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