On an application of higher energies to Sidon sets

2021/03/26 by Ilya D. Shkredov, Shkredov, Ilya D. · 1 citation
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.2103.14670

15 pages

arxiv created 2021/03/26 · openalex publication_date 2021/03/26 · arxiv updated 2021/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any finite set A and an arbitrary ε>0 there is k=k(ε) such that the higher energy E_k(A) is at most |A|^k+ε unless A has a very specific structure. As an application we obtain that any finite subset A of the real numbers or the prime field either contains an additive Sidon--type subset of size |A|^1/2+c or a multiplicative Sidon--type subset of size |A|^1/2+c.

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