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PreprintCC0arXiv

On a question of Gowers related to Littlewood's conjecture

  • Frederik Broucke
  • Máté Matolcsi
  • Szilárd Gy. Révész
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Abstract

In a blogpost in 2009, Gowers raised a possible approach to Littlewood's conjecture in Diophantine approximation, leading to a question about the existence of sufficiently many points in the unit cube such that the ``hyperbolic distance" between any two of them is large. In this note we answer this question by an explicit construction. This shows that this approach to prove Littlewood's conjecture cannot work, unless some further refinements are added.

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Cite

BibTeXRIS
BibTeX
@misc{broucke2026question,
  title = {{On a question of Gowers related to Littlewood's conjecture}},
  author = {Frederik Broucke and Máté Matolcsi and Szilárd Gy. Révész},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.27780},
  eprint = {2607.27780},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.27780},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - On a question of Gowers related to Littlewood's conjecture
AU  - Frederik Broucke
AU  - Máté Matolcsi
AU  - Szilárd Gy. Révész
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2607.27780
UR  - https://arxiv.org/abs/2607.27780
AB  - In a blogpost in 2009, Gowers raised a possible approach to Littlewood's conjecture in Diophantine approximation, leading to a question about the existence of sufficiently many points in the unit cube such that the ``hyperbolic distance" between any two of them is large. In this note we answer this question by an explicit construction. This shows that this approach to prove Littlewood's conjecture cannot work, unless some further refinements are added.
ER  -