PreprintCC BY 4.0arXiv
Inhomogeneous Fiber Refinement of Gallagher's Theorem
Abstract
Let s>0, α,γ∈ℝ, and let ψ: ℕ→ℝ>0 be a non-increasing function. Consider the limsup set Ws(ψ,α,γ) = { β∈[0,1] : normnβ−γ < ψ(n)/(normnα s) for infinitely many n∈ℕ }. Chow [Duke J. Math. 2018] settled the measure-theoretic result for s=1. In this paper, we investigate the Lebesgue measure of Ws(ψ,α,γ) for general s>0.
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BibTeX
@misc{li2026inhomogeneous,
title = {{Inhomogeneous Fiber Refinement of Gallagher's Theorem}},
author = {Qian Li and Bo Tan and Qing-Long Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01781},
eprint = {2611.01781},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01781},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inhomogeneous Fiber Refinement of Gallagher's Theorem
AU - Qian Li
AU - Bo Tan
AU - Qing-Long Zhou
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01781
UR - https://arxiv.org/abs/2611.01781
AB - Let s>0, α,γ∈ℝ, and let ψ: ℕ→ℝ_>0 be a non-increasing function. Consider the limsup set W_s(ψ,α,γ) = { β∈[0,1] : normnβ−γ < ψ(n)/(normnα^ s) for infinitely many n∈ℕ }. Chow [Duke J. Math. 2018] settled the measure-theoretic result for s=1. In this paper, we investigate the Lebesgue measure of W_s(ψ,α,γ) for general s>0.
ER -