Gasper和Rahman的二次和的新q同余

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-03 DOI:10.1016/j.jmaa.2025.129558

Victor J.W. Guo, Xing-Ye Zhu

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引用次数: 0

摘要

利用Gasper和Rahman的二次求和、第一作者和祖德林提出的创造性的显微镜观察方法以及多项式的中国剩余定理，我们以环切多项式的四次幂为模，给出了两个新的q-同余，以及一个dwork型q-同余。我们的结果是由He和Wang最近的两个q同余的推广。我们还提出了关于同余和q同余的四个相关猜想。

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New q-congruences from a quadratic summation of Gasper and Rahman

By making use of Gasper and Rahman's quadratic summation, the creative microscoping method introduced by the first author and Zudilin, and the Chinese remainder theorem for polynomials, we present two new q-congruences modulo the fourth power of a cyclotomic polynomial, along with a Dwork-type q-congruence. Our results are generalizations of two recent q-congruences due to He and Wang. We also propose four related conjectures on congruences and q-congruences.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.