Um estudo sobre o número máximo de pontos F_q-racionais em uma hipersuperfície de P^n - Ferreira, Walteir de Paula (2021)
In this work, we study the maximum number of F_q-rational points on a hypersurface of P^n . Given that some particular examples occur on general context, hypersurfaces of degree d ≥ q that vanish on all F_q-rational points, it seems reasonable to analyze separately the case of non-singular hypersurfaces of degree d, but it makes our problem much more difficult. For the case n = 2, we present the well-known Hasse-Weil Theorem. We finish the work presenting the answer given, recently, by Mrinmoy Datta at [9] for the case n = 4 and under some restrictions on d.