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arXiv · 2502.12727

An improved bound on the number of dot products determined by a finite point set in the plane

Michalis Kokkinos
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Abstract

We are interested to bound from below the number of distinct dot products determined by a finite set of points $P$ in the Euclidean plane. In this paper, we build on the work of B. Hanson, O. Roche-Newton, and S. Senger, to obtain the improved lower bound \[|\{p\cdot q : p,q\in P\}|\gtrsim |P|^{\frac2 3 + \frac{7}{1425}}.\]

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Michalis Kokkinos. 2026-06-12. An improved bound on the number of dot products determined by a finite point set in the plane. https://arxiv.org/abs/2502.12727

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