On the Hermitian curve and its intersections with some conics
  We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In particular, we provide explicit counting formulas that have also applications to some Hermitian codes. 
Chiara Marcolla, Marco Pellegrini, Massimiliano Sala
math.AC