paper

On the density of rational lines on diagonal cubic hypersurfaces, II

arXiv:2605.30549

Abstract

In this paper, we establish the expected asymptotic formula for the number of rational lines on a diagonal cubic hypersurface in 18 or more variables, improving on recent work of the second author. This is achieved via a refined mean value estimate for minor arcs that non-trivially exploits a shifting variables argument in both underlying dimensions.

Bull. Lond. Math. Soc (accepted), all comments are welcome!