q-Supercongruences for multidimensional series modulo the sixth power of a cyclotomic polynomial

2024/08/04 by Chuanan Wei, Wei, Chuanan
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.02002

openalex publication_date 2024/08/04 · openalex created_date 2024/10/14 · openalex updated_date 2026/07/28

Abstract

With the help of El Bachraoui's lemma, the creative microscoping method, and a new form of the Chinese remainder theorem for coprime polynomials, we prove a q-supercongruence for double series and a q-supercongruence for triple series modulo the sixth power of a cyclotomic polynomial. As conclusions, two corresponding supercongruences for double and triple series, which are associated with the (D.2) supercongruence of Van Hamme, are given.

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