{"title":"两个奇特的 q 超共轭及其扩展","authors":"Haihong He, Xiaoxia Wang","doi":"10.1515/forum-2023-0164","DOIUrl":null,"url":null,"abstract":"We prove two single-parameter <jats:italic>q</jats:italic>-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the <jats:italic>q</jats:italic>-binomial theorem, a Karlsson–Minton-type summation formula due to Gasper, and the method of “creative microscoping” developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang and Wang is also confirmed by establishing its <jats:italic>q</jats:italic>-analogue.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"16 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two curious q-supercongruences and their extensions\",\"authors\":\"Haihong He, Xiaoxia Wang\",\"doi\":\"10.1515/forum-2023-0164\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove two single-parameter <jats:italic>q</jats:italic>-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the <jats:italic>q</jats:italic>-binomial theorem, a Karlsson–Minton-type summation formula due to Gasper, and the method of “creative microscoping” developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang and Wang is also confirmed by establishing its <jats:italic>q</jats:italic>-analogue.\",\"PeriodicalId\":12433,\"journal\":{\"name\":\"Forum Mathematicum\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum Mathematicum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/forum-2023-0164\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Forum Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/forum-2023-0164","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Two curious q-supercongruences and their extensions
We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the q-binomial theorem, a Karlsson–Minton-type summation formula due to Gasper, and the method of “creative microscoping” developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang and Wang is also confirmed by establishing its q-analogue.
期刊介绍：
Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.
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