{"title":"外推乘法函数的均值","authors":"P.D.T.A. Elliott","doi":"10.1016/1385-7258(89)90004-8","DOIUrl":null,"url":null,"abstract":"<div><p>It is shown that certain commonly occurring conditions may be factored out of sums of multiplicative arithmetic functions.</p><p>A function is <em>arithmetic</em> if it is defined on the positive integers. Those complex-valued arithmetic functions g which satisfy the relation <em>g</em>(<em>ab</em>) = <em>g</em>(<em>a</em>)<em>g</em>(<em>b</em>) for all coprime pairs of positive integers a, b are here called <em>multiplicative</em>. In this paper <em>g</em> will be a multiplicative function which satisfies |<em>g</em>(<em>n</em>)| ≤ 1 for all positive integers <em>n</em>.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 4","pages":"Pages 409-420"},"PeriodicalIF":0.0000,"publicationDate":"1989-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(89)90004-8","citationCount":"24","resultStr":"{\"title\":\"Extrapolating the mean-values of multiplicative functions\",\"authors\":\"P.D.T.A. Elliott\",\"doi\":\"10.1016/1385-7258(89)90004-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is shown that certain commonly occurring conditions may be factored out of sums of multiplicative arithmetic functions.</p><p>A function is <em>arithmetic</em> if it is defined on the positive integers. Those complex-valued arithmetic functions g which satisfy the relation <em>g</em>(<em>ab</em>) = <em>g</em>(<em>a</em>)<em>g</em>(<em>b</em>) for all coprime pairs of positive integers a, b are here called <em>multiplicative</em>. In this paper <em>g</em> will be a multiplicative function which satisfies |<em>g</em>(<em>n</em>)| ≤ 1 for all positive integers <em>n</em>.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"92 4\",\"pages\":\"Pages 409-420\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/1385-7258(89)90004-8\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/1385725889900048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/1385725889900048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Extrapolating the mean-values of multiplicative functions
It is shown that certain commonly occurring conditions may be factored out of sums of multiplicative arithmetic functions.
A function is arithmetic if it is defined on the positive integers. Those complex-valued arithmetic functions g which satisfy the relation g(ab) = g(a)g(b) for all coprime pairs of positive integers a, b are here called multiplicative. In this paper g will be a multiplicative function which satisfies |g(n)| ≤ 1 for all positive integers n.
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