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Abstract <p> By making use of Watson’s <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(_8\phi_7\)</EquationSource> </InlineEquation> transformation and the Chinese remainder theorem for coprime polynomials, we obtain a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-congruence modulo the fourth power of a cyclotomic polynomial, which leads us to a new <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-congruence on double sums. </p>

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A New \(q\)-Congruence on Double Sums

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • H. Song,
  • C. Wang

摘要

Abstract

By making use of Watson’s \(_8\phi_7\) transformation and the Chinese remainder theorem for coprime polynomials, we obtain a \(q\) -congruence modulo the fourth power of a cyclotomic polynomial, which leads us to a new \(q\) -congruence on double sums.