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On the cardinality of the exception set in Littlewood's discrete conjecture

  • A. A. Illarionov
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Abstract

Let p be a prime, d≥ 2, H∈ [1,p), and lnln p = o(ln H). We prove that min1≤ n ≤ H n |(a1 n)/p|… |(ad n)/p| ≈ 1/((ln p)d−1 ln H) for "almost all" a ∈ (Bbb Z / pBbb Z)d.

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Cite

BibTeXRIS
BibTeX
@misc{illarionov2026cardinality,
  title = {{On the cardinality of the exception set in Littlewood's discrete conjecture}},
  author = {A. A. Illarionov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08724},
  eprint = {2609.08724},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08724},
}
RIS
TY  - UNPB
TI  - On the cardinality of the exception set in Littlewood's discrete conjecture
AU  - A. A. Illarionov
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.08724
UR  - https://arxiv.org/abs/2609.08724
AB  - Let p be a prime, d≥ 2, H∈ [1,p), and lnln p = o(ln H). We prove that min_1≤ n ≤ H n |(a_1 n)/p|… |(a_d n)/p| ≈ 1/((ln p)^d−1 ln H) for "almost all" a ∈ (Bbb Z / pBbb Z)^d.
ER  -