The Variance of the Sum of Two Squares over Intervals in ${\mathbb{F}}_q[T]$: I

Michael Yiasemides

For $B\in {\mathbb{F}}_q[T]$ of degree $2n\ge 2$, consider the number of ways of writing $B=E^2+\gamma F^2$, where $\gamma \in {\mathbb{F}}_q^{\ast }$ is fixed, and $E,F\in {\mathbb{F}}_q[T]$ with…