On Covering Systems of Polynomial Rings Over Finite Fields

Huixi Li, Nankai University

In 1950, Erd\H{o}s posed a question known as the minimum modulus problem on covering systems for $\mathbb{Z}$, which asked whether the minimum modulus of a covering system with distinct moduli is bounded. This long-standing problem was finally resolved by Hough in 2015. In this presentation, we will discuss the analogous minimum modulus problem for $\mathbb{F}_q[x]$. We proof that the smallest degree of the moduli in any covering system for $\mathbb{F}_q[x]$ of multiplicity $s$ is bounded by a constant depending only on $s$ and $q$. This is a joint work with Shaoyun Yi, Biao Wang, and Chunlin Wang. 

Zoom: https://uwaterloo.zoom.us/j/98950813087?pwd=SEl1NlNqNHl0QzlYNGJzeDVla204QT09