Some q-analogues of supercongruences for truncated $$_3F_2$$ hypergeometric series

Autor: Victor J. W. Guo
Rok vydání: 2021
Předmět:
Zdroj: The Ramanujan Journal. 59:131-142
ISSN: 1572-9303
1382-4090
DOI: 10.1007/s11139-021-00478-9
Popis: In 2003, Rodriguez–Villegas found four supercongruences modulo $$p^2$$ (p is an odd prime) for truncated $$_3F_2$$ hypergeometric series related to Calabi–Yau manifolds of dimension $$d=3$$ . One of them was already proved by Van Hamme in 1997. A q-analogue of Van Hamme’s supercongruence was given by the author and Zeng, and the author and Zudilin. In this paper, we give q-analogues of the other three supercongruences of Rodriguez–Villegas. As a conclusion, we also generalize half of Rodriguez–Villegas’s supercongruences to the modulus $$p^3$$ case.
Databáze: OpenAIRE
Externí odkaz: