Year: 2026
Type: preprint
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 [Moe26a, Conjecture 1.4] on the $a$-invariant and the $b$-invariant.
Source: arXiv (Cornell University)
Author: Ito, Haruki
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162123568