Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONSTRUCTION OF A MATTILA-SJÖLIN TYPE FUNCTION OVER A FINITE FIELD

  • Daewoong Cheong (Department of Mathematics Chungbuk National University) ;
  • Jinbeom Kim (Department of Mathematics Chungbuk National University)
  • Received : 2022.07.06
  • Accepted : 2022.08.30
  • Published : 2023.07.01
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Abstract

Let 𝔽q be a finite field with q elements. A function f : 𝔽qd × 𝔽qd → 𝔽q is called a Mattila-Sjölin type function of index γ ∈ ℝ if γ is the smallest real number such that whenever |E| ≥ Cqγ for a sufficiently large constant C, the set f(E, E) := {f(x, y) : x, y ∈ E} is equal to 𝔽q. In this article, we construct an example of a Mattila-Sjölin type function f and provide its index, generalizing the result of Cheong, Koh, Pham and Shen [1].

Keywords

Acknowledgement

This work was supported by Basic Science Research Programs through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2021R1I1A3049181).

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