We prove a two-parameter family of $q$-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews' multiseries extension of the Watson transformation, and a Karlsson--Minton type summation for very-well-poised basic hypergeometric series due to George Gasper. The new family of $q$-congruences is then used to prove two conjectures posed earlier by the authors.

中文翻译：

---

以分圆多项式的四次幂为模的一系列 q 超几何同余

我们证明了以分圆多项式的四次幂为模的 $q$-超几何同余的双参数族。我们证明中的关键要素是 George Andrews 对 Watson 变换的多级数扩展，以及 George Gasper 对非常平衡的基本超几何级数的 Karlsson-Minton 型求和。然后使用新的 $q$-同余族来证明作者先前提出的两个猜想。