The Hasse Norm Principle in Global Function Fields

Abstract

Let $L$ be a finite extension of ${\mathbb{F}}_q(t)$. We calculate the proportion of polynomials of degree $d$ in ${\mathbb{F}}_q[t]$ that are everywhere locally norms from $L/{\mathbb{F}}_q(t)$ which fail to be global norms from $L/{\mathbb{F}}_q(t)$.