arXiv
Open Access
2024
On a conjecture of Wooley and lower bounds for cubic hypersurfaces
V. Vinay Kumaraswamy
Nick Rome
Abstrak
Let $X \subset \mathbf{P}_{\mathbf{Q}}^{n-1}$ be a cubic hypersurface cut out by the vanishing of a non-degenerate rational cubic form in $n$ variables. Let $N(X,B)$ denote the number of rational points on $X$ of height at most $B$. In this article we obtain lower bounds for $N(X,B)$ for cubic hypersufaces, provided only that $n$ is large enough. In particular, we show that $N(X,B) \gg B^{n-9}$ if $n \geq 39$, thereby proving a conjecture of T. D. Wooley for non-conical cubic hypersurfaces with large enough dimension.
Topik & Kata Kunci
Penulis (2)
V
V. Vinay Kumaraswamy
N
Nick Rome
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2024
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- en
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- arXiv
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- Open Access ✓