Functions with large additive energy supported on a Hamming Sphere

2018/05/14 by James Aaronson, Aaronson, James
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1805.05295

openalex publication_date 2018/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove that, among functions f supported on a Hamming Sphere in \mathbbF₂ⁿ with fixed ℓ² norm, the additive energy is maximised when f is constant. This answers a question asked by Kirshner and Samorodnitsky.

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