Nearly sharp Lang–Weil bounds for a hypersurface
Kaloyan Slavov · Canadian Mathematical Bulletin · 2022
Abstract We improve to nearly optimal the known asymptotic and explicit bounds for the number of $\mathbb {F}_q$ -rational points on a geometrically irreducible hypersurface over a (large) finite field. The proof involves a Bertini-type probabilistic combinatorial technique. Namely, we slice the given hypersurface with a random plane.