Pinned algebraic distances determined by Cartesian products in $\mathbb{F}_p^2$

Giorgis Petridis

Pinned algebraic distances determined by Cartesian products in $\mathbb{F}_p^2$

Combinatorics 2018-11-08 v2

Authors: Giorgis Petridis

Abstract

Let $p$ be an odd prime and $A \subseteq \mathbb{F}_p$ be a subset of the finite field with $p$ elements. We show that $A \times A \subseteq \mathbb{F}_p^2$ determines at least a constant multiple of $\min\{p, |A|^{3/2}\}$ distinct pinned algebraic distances.

Keywords

pinned algebraic distances Cartesian products finite fields Erdős-type problems combinatorial geometry

Cite

@article{arxiv.1610.03172,
  title  = {Pinned algebraic distances determined by Cartesian products in $\mathbb{F}_p^2$},
  author = {Giorgis Petridis},
  journal= {arXiv preprint arXiv:1610.03172},
  year   = {2018}
}

Comments

9 pages. Minor corrections compared to the first version

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