Two q-supercongruences from Watson’s transformation

被引:0
作者
He-Xia Ni
Li-Yuan Wang
机构
[1] Nanjing Audit University,Department of Applied Mathematics
[2] Nanjing Tech University,School of Physical and Mathematical Sciences
来源
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2022年 / 116卷
关键词
Congruence; Cyclotomic polynomial; -Binomial coefficient; Watson’s transformation; Primary 11B65; Secondary 05A10; 05A30; 11A07;
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摘要
Guo and Zudilin (Adv Math, 346: 329–358, 2019) introduced a new method called ‘creative microscoping’, to prove many q-supercongruences in a unified way. In this paper, we apply this method and Watson’s 8ϕ7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_8\phi _7$$\end{document} transformation formula to prove two q-supercongruences, which were recently conjectured by Guo and Schlosser.
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