{"title":"由无理性问题启发的超几何","authors":"C. Krattenthaler, W. Zudilin","doi":"10.2206/kyushujm.73.189","DOIUrl":null,"url":null,"abstract":"We report new hypergeometric constructions of rational approximations to Catalan's constant, $\\log2$, and $\\pi^2$, their connection with already known ones, and underlying `permutation group' structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/kyushujm.73.189","citationCount":"6","resultStr":"{\"title\":\"HYPERGEOMETRY INSPIRED BY IRRATIONALITY QUESTIONS\",\"authors\":\"C. Krattenthaler, W. Zudilin\",\"doi\":\"10.2206/kyushujm.73.189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We report new hypergeometric constructions of rational approximations to Catalan's constant, $\\\\log2$, and $\\\\pi^2$, their connection with already known ones, and underlying `permutation group' structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.2206/kyushujm.73.189\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2206/kyushujm.73.189\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/kyushujm.73.189","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying `permutation group' structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers.
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