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<p>Utilizing Gasper’s Karlsson–Minton type summation formula and the ‘creative microscoping’ method introduced by Guo and Zudilin, we first give some parametric <i>q</i>-supercongruences, which generalize a supercongruence of Deines et al. Along the same lines, we also establish two classes of parametric variants. All the <i>q</i>-results we get in this paper are modulo the square of a cyclotomic polynomial, and can be deemed extensions of several results of Guo et al.</p>

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Further q-supercongruences from Gasper’s Karlsson–Minton type summation

  • 期刊论文

  • 发表日期：

    2025年11月29日

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  • Haihong He,
  • Xiaoxia Wang

摘要

Utilizing Gasper’s Karlsson–Minton type summation formula and the ‘creative microscoping’ method introduced by Guo and Zudilin, we first give some parametric q-supercongruences, which generalize a supercongruence of Deines et al. Along the same lines, we also establish two classes of parametric variants. All the q-results we get in this paper are modulo the square of a cyclotomic polynomial, and can be deemed extensions of several results of Guo et al.