Configurations of rectangles in Fq2
Journal
FINITE FIELDS AND THEIR APPLICATIONS
Journal Volume
86
Date Issued
2023
Author(s)
Koh, D
SS LEE
Pham, T
Shen, CY
Abstract
Let Fq be a finite field of order q. In this paper, we study the distribution of rectangles in a given set in Fq2. More precisely, for any 0<δ≤1, we prove that there exists an integer q0=q0(δ) with the following property: if q≥q0 and A is a multiplicative subgroup of Fq⁎ with |A|≥q2/3, then any set S⊂Fq2 with |S|≥δq2 contains at least [Formula presented] rectangles with side-lengths in A. We also consider the case of rectangles with one fixed side-length and the other in a multiplicative subgroup A.
Subjects
Rectangles; Distances; Multiplicative subgroups; EXPONENTIAL-SUMS; MULTIPLICATIVE SUBGROUPS; VECTOR-SPACES; PRODUCTS; SUBSETS; FIELDS; ERDOS; SETS
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Type
journal article