{"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":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"2 1","pages":""},"PeriodicalIF":0.6000,"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\":50720,\"journal\":{\"name\":\"Bulletin of the Australian Mathematical Society\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Australian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0004972724000467\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0004972724000467","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","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.
期刊介绍：
Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way.
Published Bi-monthly
Published for the Australian Mathematical Society
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