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Affine Coordinate Subspaces and Strong Khintchine Convergence

  • Zirui Jiang
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Abstract

We prove that every affine coordinate subspace of positive dimension and positive codimension fails to be of strong Khintchine type for convergence. Combining this with Huang's criterion for Khintchine-type affine subspaces gives a sufficient Diophantine condition for an affine coordinate subspace to be of Khintchine type but not of strong Khintchine type for convergence.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026affine,
  title = {{Affine Coordinate Subspaces and Strong Khintchine Convergence}},
  author = {Zirui Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09017},
  eprint = {2610.09017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09017},
}
RIS
TY  - UNPB
TI  - Affine Coordinate Subspaces and Strong Khintchine Convergence
AU  - Zirui Jiang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.09017
UR  - https://arxiv.org/abs/2610.09017
AB  - We prove that every affine coordinate subspace of positive dimension and positive codimension fails to be of strong Khintchine type for convergence. Combining this with Huang's criterion for Khintchine-type affine subspaces gives a sufficient Diophantine condition for an affine coordinate subspace to be of Khintchine type but not of strong Khintchine type for convergence.
ER  -