학술저널
Note on the pinned distance problem over finite fields
Note on the pinned distance problem over finite fields
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 35, No. 3
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2022.08null - null (null pages)
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DOI : 10.14403/jcms.2022.35.3.227
- 0

Let Fq be a finite field with odd q elements. In this article, we prove that if E ⊆ Fqd , d ≥ 2, and |E| ≥ q, then thered with |Y | ∼ qd such that for all y ∈ Y , theqexists a set Y ⊆ Fnumber of distances between the point y and the set E is ∼ q. Asd with |E| ≥ q, thereqa corollary, we obtain that for each set E ⊆ Fd with |Y | ∼ qd so that any set E ∪ {y} withqexists a set Y ⊆ Fy ∈ Y determines a positive proportion of all possible distances. The averaging argument and the pigeonhole principle play a crucial role in proving our results.
1. Introduction
2. Proof of main result (Theorem 1.7)
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