On the density of rational lines on diagonal cubic hypersurfaces

Kiseok Yeon

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arXiv · 2602.04654

On the density of rational lines on diagonal cubic hypersurfaces

Kiseok Yeon

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Abstract

In this paper, we establish the asymptotic estimates for the rational lines on diagonal cubic hypersurfaces defined by $\sum_{i=1}^sc_ix^3_i=0$ with $c_i\in\mathbb{Z}\setminus \{0\},$ provided that $s\geq 19.$ This improves the previously known bound $s\geq 21$ 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.

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Kiseok Yeon. 2026-02-04. On the density of rational lines on diagonal cubic hypersurfaces. https://arxiv.org/abs/2602.04654

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