{"title":"Approximation by the Riemann zeta-function","authors":"P. Gauthier, N. Tarkhanov","doi":"10.1080/02781070412331331491","DOIUrl":null,"url":null,"abstract":"Any meromorphic function having at most simple poles can be approximated by linear combinations of translates of the Riemann zeta-function. In particular, an arbitrary holomorphic function can be so approximated. If derivatives of the zeta-function are allowed, then arbitrary meromorphic functions can be approximated.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables, Theory and Application: An International Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/02781070412331331491","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
Any meromorphic function having at most simple poles can be approximated by linear combinations of translates of the Riemann zeta-function. In particular, an arbitrary holomorphic function can be so approximated. If derivatives of the zeta-function are allowed, then arbitrary meromorphic functions can be approximated.