{"title":"具有任意参数的超几何函数的代数性","authors":"Florian Fürnsinn, Sergey Yurkevich","doi":"10.1112/blms.13103","DOIUrl":null,"url":null,"abstract":"<p>We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol and Beukers–Heckman for globally bounded and algebraic hypergeometric functions, however, in a more general setting that allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 9","pages":"2824-2846"},"PeriodicalIF":0.8000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13103","citationCount":"0","resultStr":"{\"title\":\"Algebraicity of hypergeometric functions with arbitrary parameters\",\"authors\":\"Florian Fürnsinn, Sergey Yurkevich\",\"doi\":\"10.1112/blms.13103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol and Beukers–Heckman for globally bounded and algebraic hypergeometric functions, however, in a more general setting that allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples.</p>\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"56 9\",\"pages\":\"2824-2846\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13103\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/blms.13103\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13103","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Algebraicity of hypergeometric functions with arbitrary parameters
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol and Beukers–Heckman for globally bounded and algebraic hypergeometric functions, however, in a more general setting that allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples.
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