Title: Mahler Discrete Residues and Summability for Rational Functions

Abstract: We construct Mahler discrete residues for rational functions and show that they comprise a complete obstruction to the Mahler summability problem of deciding whether a given rational function $f(x)$ is of the form $g(x^p)-g(x)$ for some rational function $g(x)$ and an integer $p > 1$. This extends to the Mahler case the analogous notions, properties, and applications of discrete residues (in the shift case) and $q$-discrete residues (in the $q$-difference case) developed by Chen and Singer. Along the way we define several additional notions that promise to be useful for addressing related questions involving Mahler difference fields of rational functions, including in particular telescoping problems and problems in the (differential) Galois theory of Mahler difference equations.

主讲人简介：张熠，2011年于苏州大学获学士学位，2016年于中国科学院数学与系统科学研究院获博士学位，2017年于奥地利约翰开普勒林茨大学获博士学位。2017年至2020年分别于奥地利科学院，美国德克萨斯大学达拉斯分校从事博士后研究。于2020年起任西交利物浦大学数学系助理教授。主要从事符号计算，算法组合，微分及差分方程的代数理论，密码学等相关理论及应用研究，在J. Symb. Comput., ISSAC, Adv. In Appl. Math., IEEE Trans. Inf. Theory等国际权威期刊和会议发表及接收论文10余篇。

报告时间：2022年9月3日10:00

报告地点：知新楼B1220、腾讯会议

邀请人：黄巧龙

联系人：黄巧龙，联系方式：huangqiaolong@sdu.edu.cn