Sums of transcendental dilates

2022/12/20 by David Conlon, Conlon, David, Jeck Lim +1 · 1 citation
Mathematics · #05D99 #11B13 #11B30 #11B75 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2212.10128

openalex publication_date 2022/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that there is an absolute constant c>0 such that |A+λ⋅ A|≥ e^{c√(log |A|)}|A| for any finite subset A of ℝ and any transcendental number λ∈ℝ. By a construction of Konyagin and Laba, this is best possible up to the constant c.

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