Year: 2026
Type: preprint
Abstract: We use the circle method to count $\mathbb{F}_q(t)$-rational points of bounded naive height on a quadric hypersurface $X\subseteq \mathbb{P}^{n-1}$ defined over $\mathbb{F}_q$, provided that $\mathrm{char}(\mathbb{F}_q)>2$ and $n\ge 3$. Viewing these points as morphisms $\mathbb{P}^1 \to X$ of fixed degree, we obtain exact formulas for their number depending on the parity of $n$ and on the determinant of the quadratic form defining $X$, including secondary terms in some cases.
Source: arXiv (Cornell University)
Author: Mettasch, Johanna
Institution: Leibniz University Hannover
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7148655883
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