Interpolation of point configurations in the discrete plane

Esen Aksoy, Alex Iosevich, Brian McDonald

Defining distances over finite fields formally by $||x-y||:=(x_1-y_1{)}^2+\cdots +(x_d-y_d{)}^2$ for $x,y\in {\mathbb{F}}_q^d$, distance problems naturally arise in analogy to those stu…