Mathematics > Number Theory
arXiv:2603.16794 (math)
[Submitted on 17 Mar 2026 (v1), last revised 17 Jun 2026 (this version, v3)]
Abstract:We prove that for any real number $\xi\neq 0$ and any coprime integers $p>q\ge1$ such that $\xi$ is irrational or $q>1$, the image in $\mathbb{R}/\mathbb{Z}$ of the sequence $(\xi (-p/q)^n)_{n\ge 0}$ is not contained in any interval of length less than $(1+q/p-q^2/p^2)/p$.
Submission history
From: Weizhe Zheng [view email]
[v1]
Tue, 17 Mar 2026 17:03:45 UTC (8 KB)
[v2]
Tue, 24 Mar 2026 05:18:13 UTC (8 KB)
[v3]
Wed, 17 Jun 2026 06:25:00 UTC (8 KB)
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