On the density of rational lines on diagonal cubic hypersurfaces
Number Theory
2026-02-05 v1
Abstract
In this paper, we establish the asymptotic estimates for the rational lines on diagonal cubic hypersurfaces defined by with provided that This improves the previously known bound required to obtain such asymptotic estimates. Our approach develops a multidimensional shifting variables argument together with a pruning argument, and exploits the recent progress on the Parsell-Vinogradov system.
Keywords
Cite
@article{arxiv.2602.04654,
title = {On the density of rational lines on diagonal cubic hypersurfaces},
author = {Kiseok Yeon},
journal= {arXiv preprint arXiv:2602.04654},
year = {2026}
}
Comments
14 pages, all comments welcome!