Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields
Number Theory
2026-05-12 v1 Algebraic Geometry
Abstract
We improve a bound due to the second author on number of rational points on smooth surfaces in over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact number of rational points. These computations may have independent interest.
Cite
@article{arxiv.2605.09166,
title = {Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields},
author = {Yves Aubry and José Felipe Voloch},
journal= {arXiv preprint arXiv:2605.09166},
year = {2026}
}