Polynomial reduction and supercongruences. (March 2021)

• Record Type: Journal Article
• Authors: Hou, Qing-Hu; Mu, Yan-Ping; Zeilberger, Doron
• Is Part Of: Journal of symbolic computation. Volume 103(2021)
• Page Start: 127
• Page End: 140
• Publication Date: 2021-03
• Subjects: Hypergeometric term -- Supercongruence -- Polynomial reduction; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.11.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Based on a reduction process, we rewrite a hypergeometric term as the sum of the difference of a hypergeometric term and a reduced hypergeometric term (the reduced part, in short). We show that when the initial hypergeometric term has a certain kind of symmetry, the reduced part contains only odd or even powers. As applications, we derived two infinite families of supercongruences.