Hanfei Song, Chun Wang: Some $q$-congruences related to double sums, 71-78

Abstract:

In this paper, we provide two new $q$-congruences associated with double basic hypergeometric sums. A related conjecture on $q$-congruences modulo the cube and fourth powers of a cyclotomic polynomial is also proposed.

Key Words: $q$-congruences, supercongruences, cyclotomic polynomial, basic hypergeometric series.

2020 Mathematics Subject Classification: Primary 11A07; Secondary 11B65.

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