On a question of Davenport and diagonal cubic forms over ${\mathbb{F}}_q(t)$

Jakob Glas, Leonhard Hochfilzer

Given a non-singular diagonal cubic hypersurface $X\subset {\mathbb{P}}^{n-1}$ over ${\mathbb{F}}_q(t)$ with $\mathrm{char}({\mathbb{F}}_q)\ne 3$, we show that the number of rational po…