Bivariate trinomials over finite fields

Martin Avendano, Jorge Martin-Morales

We study the number of points in the family of plane curves defined by a trinomial \[ \mathcal{C}(α,β)= \{(x,y)\in\mathbb{F}_q^2\,:\,αx^{a_{11}}y^{a_{12}}+βx^{a_{21}}y^{a_{22}}=x^{…