Some supercongruences arising from symbolic summation

2019/12/02 by Ji-Cai Liu, Liu, Ji-Cai
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1912.00663

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on some combinatorial identities arising from symbolic summation, we extend two supercongruences on partial sums of hypergeometric series, which were originally conjectured by Guo and Schlosser and recently confirmed by Jana and Kalita.

Citations

• A q-microscope for supercongruences
• Some supercongruences occurring in truncated hypergeometric series

Related

• Two supercongruences involving truncated hypergeometric series
• An extension of a supercongruence of Long and Ramakrishna
• Supercongruences arising from hypergeometric series identities
• On supercongruences for truncated sums of squares of basic hypergeometric series
• Generalizations of two hypergeometric sums related to conjectures of Guo