Upper bounds on pairs of dot products

2015/02/05 by Daniel W. Barker, Barker, Daniel, Steven Senger +1 · 2 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1502.01729

openalex publication_date 2015/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a large finite point set, P⊂ \mathbb R², we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, (α, β), we bound the size of the set \(p,q,r)∈ P × P × P : p ⋅ q = α, p ⋅ r = β\.

Cited by

• A Density Condition on Point Sets with Slowly-Scaling Distinct Dot Products
• Incidences and pairs of dot products

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