{"title":"由安德鲁斯的身份产生的 q 级超不确定性","authors":"JI-CAI LIU, JING LIU","doi":"10.1017/s0004972724000467","DOIUrl":null,"url":null,"abstract":"We establish a <jats:italic>q</jats:italic>-analogue of a supercongruence related to a supercongruence of Rodriguez-Villegas, which extends a <jats:italic>q</jats:italic>-congruence of Guo and Zeng [‘Some <jats:italic>q</jats:italic>-analogues of supercongruences of Rodriguez-Villegas’, <jats:italic>J. Number Theory</jats:italic>145 (2014), 301–316]. The important ingredients in the proof include Andrews’ <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000467_inline2.png\"/> <jats:tex-math> $_4\\phi _3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> terminating identity.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A q-SUPERCONGRUENCE ARISING FROM ANDREWS’ IDENTITY\",\"authors\":\"JI-CAI LIU, JING LIU\",\"doi\":\"10.1017/s0004972724000467\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish a <jats:italic>q</jats:italic>-analogue of a supercongruence related to a supercongruence of Rodriguez-Villegas, which extends a <jats:italic>q</jats:italic>-congruence of Guo and Zeng [‘Some <jats:italic>q</jats:italic>-analogues of supercongruences of Rodriguez-Villegas’, <jats:italic>J. Number Theory</jats:italic>145 (2014), 301–316]. The important ingredients in the proof include Andrews’ <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0004972724000467_inline2.png\\\"/> <jats:tex-math> $_4\\\\phi _3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> terminating identity.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0004972724000467\",\"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/10.1017/s0004972724000467","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们建立了一个与罗德里格斯-维耶加斯的超等公差相关的 q-analogue ，它扩展了郭和曾的 q-ongruence ['罗德里格斯-维耶加斯的超等公差的一些 q-analogue', J. Number Theory145 (2014), 301-316] 。证明中的重要成分包括安德鲁斯的$_4\phi _3$终止身份。
A q-SUPERCONGRUENCE ARISING FROM ANDREWS’ IDENTITY
We establish a q-analogue of a supercongruence related to a supercongruence of Rodriguez-Villegas, which extends a q-congruence of Guo and Zeng [‘Some q-analogues of supercongruences of Rodriguez-Villegas’, J. Number Theory145 (2014), 301–316]. The important ingredients in the proof include Andrews’ $_4\phi _3$ terminating identity.
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