Rational points on complete intersections of cubic and quadric hypersurfaces over F q ( t ) $\mathbb {F}_q(t)$

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 $F_q\left(t\right)$, provided $char\left(F_q\right)>3$. Under the same hypotheses, we also verify weak approximation.