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<p>We deduce a new family of <i>q</i>-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews’ multi-series extension of the Watson transformation. A Karlsson–Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and <i>q</i>-supercongruences for further study.</p>

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A new family of q-hypergeometric congruences from Andrews’ multi-series transformation

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  • 发表日期：

    2025年4月10日

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  • Victor J. W. Guo,
  • Michael J. Schlosser

摘要

We deduce a new family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews’ multi-series extension of the Watson transformation. A Karlsson–Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and q-supercongruences for further study.