{"title":"关于乘法函数和的一个猜想","authors":"S. T. Tulyaganov","doi":"10.1070/SM1992V071N02ABEH002133","DOIUrl":null,"url":null,"abstract":"We consider the following conjecture, which was made in 1970 by B. V. Levin and A. S. Faĭnleĭb; if , , , and (2) is fulfilled with , then (1) holds. We prove that this conjecture holds if . In the case we construct a counterexample to the conjecture. The asymptotic behavior of the sum of values of the function is found by an analytic method.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON A CONJECTURE ON SUMS OF MULTIPLICATIVE FUNCTIONS\",\"authors\":\"S. T. Tulyaganov\",\"doi\":\"10.1070/SM1992V071N02ABEH002133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the following conjecture, which was made in 1970 by B. V. Levin and A. S. Faĭnleĭb; if , , , and (2) is fulfilled with , then (1) holds. We prove that this conjecture holds if . In the case we construct a counterexample to the conjecture. The asymptotic behavior of the sum of values of the function is found by an analytic method.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V071N02ABEH002133\",\"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 of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N02ABEH002133","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON A CONJECTURE ON SUMS OF MULTIPLICATIVE FUNCTIONS
We consider the following conjecture, which was made in 1970 by B. V. Levin and A. S. Faĭnleĭb; if , , , and (2) is fulfilled with , then (1) holds. We prove that this conjecture holds if . In the case we construct a counterexample to the conjecture. The asymptotic behavior of the sum of values of the function is found by an analytic method.
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