https://scholars.lib.ntu.edu.tw/handle/123456789/631778
Title: | Configurations of rectangles in Fq2 | Authors: | Koh, D SS LEE Pham, T Shen, CY |
Keywords: | Rectangles; Distances; Multiplicative subgroups; EXPONENTIAL-SUMS; MULTIPLICATIVE SUBGROUPS; VECTOR-SPACES; PRODUCTS; SUBSETS; FIELDS; ERDOS; SETS | Issue Date: | Feb-2023 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal Volume: | 86 | Source: | FINITE FIELDS AND THEIR APPLICATIONS | 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. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/631778 | ISSN: | 1071-5797 | DOI: | 10.1016/j.ffa.2022.102147 |
Appears in Collections: | 數學系 |
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