Sum-Product Type Estimates for Subsets of Finite Valuation Rings

2017/01/27 by Esen Aksoy Yazici, Yazici, Esen Aksoy
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1701.08101

openalex publication_date 2017/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a finite valuation ring of order q^r. Using a point-plane incidence estimate in R³, we obtain sum-product type estimates for subsets of R. In particular, we prove that for A⊂ R, |AA+A|≫ min\q^r, \frac|A|³q^2r-1\. We also show that if |A+A||A|²>q^3r-1, then |A²+A²||A+A|≫ q^(r)/(2)|A|^(3)/(2).

Citations

• Products of Differences in Prime Order Finite Fields

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