{"title":"涉及Domb数和二元二次型的超同余。","authors":"Guo-Shuai Mao, Michael J Schlosser","doi":"10.1007/s13398-023-01509-4","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we prove two recently conjectured supercongruences (modulo <math><msup><mi>p</mi><mn>3</mn></msup></math>, where <i>p</i> is any prime greater than 3) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomials, harmonic numbers, binomial coefficients, and hypergeometric summations and transformations.</p>","PeriodicalId":54471,"journal":{"name":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","volume":"118 1","pages":"11"},"PeriodicalIF":1.8000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10547664/pdf/","citationCount":"0","resultStr":"{\"title\":\"Supercongruences involving Domb numbers and binary quadratic forms.\",\"authors\":\"Guo-Shuai Mao, Michael J Schlosser\",\"doi\":\"10.1007/s13398-023-01509-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper, we prove two recently conjectured supercongruences (modulo <math><msup><mi>p</mi><mn>3</mn></msup></math>, where <i>p</i> is any prime greater than 3) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomials, harmonic numbers, binomial coefficients, and hypergeometric summations and transformations.</p>\",\"PeriodicalId\":54471,\"journal\":{\"name\":\"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas\",\"volume\":\"118 1\",\"pages\":\"11\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10547664/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13398-023-01509-4\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/10/3 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13398-023-01509-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/10/3 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Supercongruences involving Domb numbers and binary quadratic forms.
In this paper, we prove two recently conjectured supercongruences (modulo , where p is any prime greater than 3) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomials, harmonic numbers, binomial coefficients, and hypergeometric summations and transformations.
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The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.
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