Ji-Cai Liu

collaborators

3 papers

math.NT2026

Two $q$ -congruences from Jackson's $_{8} ϕ_{7}$ summation and Andrews' $_{4} ϕ_{3}$ summation

Ji-Cai Liu, Qing-Yuan Tao

We prove two $q$ -congruence conjectures of Guo on truncated basic hypergeometric series. The first result strengthens a congruence obtained from Jackson's terminating very-well-poi…

math.NT2026

Proofs of two $q$ -congruence conjectures of Guo

Ji-Cai Liu, Qing-Yuan Tao

We prove two conjectural $q$ -congruences proposed by Guo. The first is Conjecture 7.2 in Guo's work on $q$ -analogues of two ``divergent'' Ramanujan-type supercongruences; it assert…

math.NT2024

On the positive coefficients of two families of $q$ -series

Ji-Cai Liu, Kong-Lian Liao

Let $S$ be a finite set of pairwise coprime positive integers and $A x^{2} + B x$ be an integer valued polynomial with $A > B \geq 0$ . For integers $k \geq 1$ and $n \geq 0$ , the coefficients $…

Two q-congruences from Jackson's 8​ϕ7​ summation and Andrews' 4​ϕ3​ summation

Proofs of two q-congruence conjectures of Guo

On the positive coefficients of two families of q-series

Two $q$ -congruences from Jackson's $_{8} ϕ_{7}$ summation and Andrews' $_{4} ϕ_{3}$ summation

Proofs of two $q$ -congruence conjectures of Guo

On the positive coefficients of two families of $q$ -series