{"title":"微分算子的特征值与黎曼$\\zeta$-函数的零点","authors":"L. Ge","doi":"10.4208/ata.oa-su1","DOIUrl":null,"url":null,"abstract":"The eigenvalues of a differential operator on a Hilbert-Pólya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ζ-function. Moreover, their corresponding multiplicities are the same.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"132 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Eigenvalues of a Differential Operator and Zeros of the Riemann $\\\\zeta$-Function\",\"authors\":\"L. Ge\",\"doi\":\"10.4208/ata.oa-su1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The eigenvalues of a differential operator on a Hilbert-Pólya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ζ-function. Moreover, their corresponding multiplicities are the same.\",\"PeriodicalId\":29763,\"journal\":{\"name\":\"Analysis in Theory and Applications\",\"volume\":\"132 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis in Theory and Applications\",\"FirstCategoryId\":\"95\",\"ListUrlMain\":\"https://doi.org/10.4208/ata.oa-su1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis in Theory and Applications","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.4208/ata.oa-su1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function
The eigenvalues of a differential operator on a Hilbert-Pólya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ζ-function. Moreover, their corresponding multiplicities are the same.
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