Fermat vs Waring: an introduction to number theory in function fields

Abstract: Let $\Z$ be the ring of integers, and let $\mathbb{F}_p[t]$ be the ring of polynomials in one variable defined over the finite field $\mathbb{F}_p$ of $p$ elements. Since the characteristic of $\Z$ is $0$, while that of $\mathbb{F}_p[t]$ is the positive prime number $p$, it is a striking theme in arithmetic that these two rings faithfully resemble each other. The study of the similarity and difference between $\Z$ and $\mathbb{F}_p[t]$ lies in the field that relates number fields to function fields. In this talk, we will investigate some Diophantine problems in the settings of $\Z$ and $\mathbb{F}_p[t]$, including Fermat's Last Theorem and Waring's problem.

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar