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PreprintCC BY-NC-ND 4.0arXiv

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

  • Haruki Ito
Open at sourcePDFDOICite

Abstract

Let k be a positive integer and let Xk be the cubic hypersurface defined by the equation x3−(y12+⋯+y4k2)z=0. In this paper, we give an asymptotic formula for the counting function of semi-integral points on Xk. We also prove that this asymptotic formula agrees with Manin's conjecture for ℳ-points [Moe26a, Conjecture 1.4] on the a-invariant and the b-invariant.

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Cite

BibTeXRIS
BibTeX
@misc{ito2026distribution,
  title = {{The distribution of semi-integral points on a class of singular cubic hypersurfaces}},
  author = {Haruki Ito},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.22371},
  eprint = {2605.22371},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.22371},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The distribution of semi-integral points on a class of singular cubic hypersurfaces
AU  - Haruki Ito
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2605.22371
UR  - https://arxiv.org/abs/2605.22371
AB  - Let k be a positive integer and let X_k be the cubic hypersurface defined by the equation x^3−(y_1^2+⋯+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 ℳ-points [Moe26a, Conjecture 1.4] on the a-invariant and the b-invariant.
ER  -