{"title":"关于Wiener-Ikehara定理和Ingham-Karamata定理中余数的不存在:一个建设性的方法","authors":"Frederik Broucke, Gregory Debruyne, J. Vindas","doi":"10.1090/proc/15320","DOIUrl":null,"url":null,"abstract":"We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"54 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: A constructive approach\",\"authors\":\"Frederik Broucke, Gregory Debruyne, J. Vindas\",\"doi\":\"10.1090/proc/15320\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).\",\"PeriodicalId\":8451,\"journal\":{\"name\":\"arXiv: Classical Analysis and ODEs\",\"volume\":\"54 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Classical Analysis and ODEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/15320\",\"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: Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15320","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: A constructive approach
We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).
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