{"title":"关于等差数列素数的Mertens定理中的常数","authors":"Keliher, Daniel, Lee, Ethan Simpson","doi":"10.48550/arxiv.2306.09981","DOIUrl":null,"url":null,"abstract":"A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of the constant in Mertens' second theorem for primes in arithmetic progressions. Assuming the Generalised Riemann Hypothesis, we make Norton's observation explicit and extend this result to multiple progressions.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"186 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the constants in Mertens' theorems for primes in arithmetic\\n progressions\",\"authors\":\"Keliher, Daniel, Lee, Ethan Simpson\",\"doi\":\"10.48550/arxiv.2306.09981\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of the constant in Mertens' second theorem for primes in arithmetic progressions. Assuming the Generalised Riemann Hypothesis, we make Norton's observation explicit and extend this result to multiple progressions.\",\"PeriodicalId\":496270,\"journal\":{\"name\":\"arXiv (Cornell University)\",\"volume\":\"186 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv (Cornell University)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arxiv.2306.09981\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv (Cornell University)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arxiv.2306.09981","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the constants in Mertens' theorems for primes in arithmetic
progressions
A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of the constant in Mertens' second theorem for primes in arithmetic progressions. Assuming the Generalised Riemann Hypothesis, we make Norton's observation explicit and extend this result to multiple progressions.
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