Sum-Product Type Estimates over Finite Fields

2019/03/19 by Esen Aksoy Yazici, Yazici, Esen Aksoy
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.07876

openalex publication_date 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbF_q denote the finite field with q elements where q=p^l is a prime power. Using Fourier analytic tools with a third moment method, we obtain sum-product type estimates for subsets of \mathbbF_q. In particular, we prove that if A⊂ \mathbbF_q, then |AA+A|,|A(A+A)|≫min\q, \frac|A|²q^(1)/(2) \, so that if A≥ q^(3)/(4), then |AA+A|,|A(A+A)|≫ q.

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