Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Biao Wang, Yunnan University
Inviter:	Doctor Li Zhang
Title:	On Erdos covering systems
Language:	Chinese
Time & Venue:	2023.09.04 10:00-11:00 Tencent Meeting: 175-737-564
Abstract:	In this talk, we will introduce the distortion method for the minimum modulus problem on covering systems. The minimum modulus problem was posed by Erd?s 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 Erd?s’ 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.