摘要

In 1880, Appell introduced four types of double series F1, F2, F3, F4 as an extension of the Gauss hypergeometric series 2F1 to two variables. These four series, called Appell series, are a fundamental class of hypergeometric functions in two variables. They play an essential role in various branches of physics, particularly in mathematical physics, quantum mechanics, and general relativity. In this paper, we present several new supercongruences related to the truncated Appell series F3. These results include two extensions of a previously established supercongruence by Lin and Liu, as well as a conjecture proposed by Wang and Yu.

报告人简介

王晓霞，博士生导师，教授，研究方向组合数学，主要从事组合恒等式、q-级数恒等式、q-同余式等相关的研究工作。主持国家自然科学基金青年项目和面上项目各一项，上海市自然科学基金青年项目和面上项目各一项。截止目前，共发表论文60余篇，主要发表在Adv. Appl. Math.、Proc. Amer. Math. Soc. 、Ramanujan J.等国际高水平杂志上。