Supercongruences involving Domb numbers and binary quadratic forms

2021/12/23 by Guo-Shuai Mao, Mao, Guo-Shuai, Michael J. Schlosser +1
Mathematics · #11A07 (Primary) 11B65 #11B83 #11E16 (Secondary) #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11A07 #msc:11B65 #msc:11B83 #msc:11E16

paper · pdf · doi:10.48550/arxiv.2112.12732

17 pp

arxiv created 2021/12/23 · openalex publication_date 2021/12/23 · arxiv updated 2021/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove two recently conjectured supercongruences (modulo p³, 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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