Complete intersections of cubic and quadric hypersurfaces over $\mathbb{F}_q(t)$

Abstract

Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least $23$ over $\mathbb{F}_q(t)$, provided $\text{cha}(\mathbb{F}_q)>3$. Under the same hypotheses, we also verify weak approximation.