从Andrews的多级数变换中得到一个新的q-超几何同余族。

IF 1.8 2区数学 Q1 MATHEMATICS

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas Pub Date : 2025-01-01 Epub Date: 2025-04-10 DOI:10.1007/s13398-025-01721-4

Victor J W Guo, Michael J Schlosser

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引用次数: 0

摘要

我们从George Andrews对Watson变换的多级数扩展中，导出了一组以环切多项式的四次幂模的q-超几何同余。由George Gasper提出的非常平衡的基本超几何级数的Karlsson-Minton型求和在我们的证明中也起了重要作用。我们提出了关于超同余和q-超同余的两个相关猜想，以供进一步研究。

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

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.

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来源期刊

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 数学-数学

CiteScore

4.70

自引率

17.20%

发文量

151

审稿时长

>12 weeks

期刊介绍： The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.