{"title":"某些数论误差项的卷积和均方估计","authors":"A. Ivic","doi":"10.2298/PIM0694141I","DOIUrl":null,"url":null,"abstract":"We study the convolution function C[f(x)]:=\\int_1^x f(y)f\\Bigl(\\frac xy\\Bigr)\\frac{dy}y When f(x) is a suitable number-theoretic error term. Asymptotics and upper bounds for C[f(x)] are derived from mean square bounds for f(x). Some applications are given, in particular to |\\zeta(\\tfrac12+ix)|^{2k} and the classical Rankin--Selberg problem from analytic number theory.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"CONVOLUTIONS AND MEAN SQUARE ESTIMATES OF CERTAIN NUMBER-THEORETIC ERROR TERMS\",\"authors\":\"A. Ivic\",\"doi\":\"10.2298/PIM0694141I\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the convolution function C[f(x)]:=\\\\int_1^x f(y)f\\\\Bigl(\\\\frac xy\\\\Bigr)\\\\frac{dy}y When f(x) is a suitable number-theoretic error term. Asymptotics and upper bounds for C[f(x)] are derived from mean square bounds for f(x). Some applications are given, in particular to |\\\\zeta(\\\\tfrac12+ix)|^{2k} and the classical Rankin--Selberg problem from analytic number theory.\",\"PeriodicalId\":416273,\"journal\":{\"name\":\"Publications De L'institut Mathematique\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-12-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Publications De L'institut Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/PIM0694141I\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/PIM0694141I","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
CONVOLUTIONS AND MEAN SQUARE ESTIMATES OF CERTAIN NUMBER-THEORETIC ERROR TERMS
We study the convolution function C[f(x)]:=\int_1^x f(y)f\Bigl(\frac xy\Bigr)\frac{dy}y When f(x) is a suitable number-theoretic error term. Asymptotics and upper bounds for C[f(x)] are derived from mean square bounds for f(x). Some applications are given, in particular to |\zeta(\tfrac12+ix)|^{2k} and the classical Rankin--Selberg problem from analytic number theory.
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