PreprintCC BY 4.0arXiv
Prime points on smooth hypersurfaces
Abstract
Let F ∈ ℤ[x1, …, xn] be a homogeneous form of degree d ≥ 4 which defines a smooth hypersurface in ℙn−1ℂ. For n ≥ 24 d4 2d, we prove an asymptotic formula for the number of prime solutions to the equation F(x1, …, xn) = 0, provided F satisfies suitable local conditions.
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BibTeX
@misc{diao2026prime,
title = {{Prime points on smooth hypersurfaces}},
author = {Yijie Diao and Shuntaro Yamagishi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09735},
eprint = {2610.09735},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09735},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prime points on smooth hypersurfaces
AU - Yijie Diao
AU - Shuntaro Yamagishi
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09735
UR - https://arxiv.org/abs/2610.09735
AB - Let F ∈ ℤ[x_1, …, x_n] be a homogeneous form of degree d ≥ 4 which defines a smooth hypersurface in ℙ^n−1_ℂ. For n ≥ 24 d^4 2^d, we prove an asymptotic formula for the number of prime solutions to the equation F(x_1, …, x_n) = 0, provided F satisfies suitable local conditions.
ER -