Sum of dilates in vector spaces

2014/10/31 by Antal Balog, Balog, Antal, George Shakan +1
Mathematics · #11B75 #Advanced Banach Space Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Holomorphic and Operator Theory #Number Theory (math.NT) #math.CO #math.NT #msc:11B75

paper · pdf · doi:10.48550/arxiv.1410.8614

arxiv created 2014/10/31 · openalex publication_date 2014/10/31 · arxiv updated 2014/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let d≥ 2, A ⊂ ℤ^d be finite and not contained in a translate of any hyperplane, and q ∈ ℤ such that |q| > 1. We show |A+ q ⋅ A| ≥ (|q|+d+1)|A| - O_q,d(1).

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