On pointless diagonal Fermat curves

We give an improved asymptotic upper bound on the number of diagonal Fermat curves $A{x}^{\mathrm{\ell }}+B{y}^{\mathrm{\ell }}=z^{\mathrm{\ell }}$ over ${\mathbb{F}}_q$ with no ${\mathbb{F}}_q$-rational points, where $\mathrm{\ell }$ is a prime number dividing $q-1$.