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arXiv · 2605.22371

The distribution of semi-integral points on a class of singular cubic hypersurfaces

Haruki Ito
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Abstract

Let $k$ be a positive integer and let $X_k$ be the cubic hypersurface defined by the equation $x^3-(y_1^2+\cdots+y_{4k}^2)z=0$. In this paper, we give an asymptotic formula for the counting function of semi-integral points on $X_k$. We also prove that this asymptotic formula agrees with Manin's conjecture for $\mathcal{M}$-points \cite[Conjecture~1.4]{Moe26a} on the $a$-invariant and the $b$-invariant.

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Haruki Ito. 2026-05-21. The distribution of semi-integral points on a class of singular cubic hypersurfaces. https://arxiv.org/abs/2605.22371

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