On the Distribution of Discriminants over a Finite Field

Jonathan Chan, Soonho Kwon, Michael Seaman

For a prime power $q$, we show that the discriminants of monic polynomials in ${\mathbb{F}}_q[x]$ of a fixed degree $m$ are equally distributed if $\gcd (q-1,m(m-1))=2$ when $q$ is od…