{"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}
引用次数: 0
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.
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