Biao Wang, Yunnan University

Li Zhang, Doctor

On Erdős covering systems

10:00-11:00 September 4 (Monday), Tencent Meeting: 175-737-564

In this talk, we will introduce the distortion method for the minimum modulus problem on covering systems. The minimum modulus problem was posed by Erdős in 1950, who asked whether the minimum modulus of a covering system with distinct moduli is uniformly bounded. In 2007, Filaseta, Ford, Konyagin, Pomerance and Yu affirmed it if the reciprocal sum of the moduli of a covering system is bounded. Later in 2015, Hough resolved this problem by showing that the minimum modulus is at most $10^{16}$. In 2022, Balister, Bollobas, Morris, Sahasrabudhe and Tiba reduced this bound to 616,000 by developing a versatile method called the distortion method. Recently, Klein, Koukoulopoulos and Lemieux generalized Hough’s result by using this method. Following Klein et al.’s work, we provide a solution to Erdős’ minimum modulus problem in number fields. This is a joint work with Huixi Li and Shaoyun Yi. Furthermore, in a recent joint work with Chunlin Wang, we provide a solution to the case finite fields.

报告人简介：王标，四川仁寿人，2011 年四川大学数学学院本科毕业,2014 年中科院数学所硕士毕业，2021 年纽约州立大学布法罗分校数学系博士毕业，2023 年 6 月中国科学院数学与系统科学研究院博士后出站，现即将入职云南大学数学与统计学院。主要研究方向为解析数论，研究成果发表于 J. Number Theory、Finite Fields Appl.、Int. J. Number Theory、RamanujanJ.等国际数学期刊。