https://scholars.lib.ntu.edu.tw/handle/123456789/624587
標題: | Mattila–Sjölin Type Functions: A Finite Field Model | 作者: | Cheong D Koh D Pham T CHUN-YEN SHEN |
關鍵字: | Erdős–Falconer distance problem; Falconer distance conjecture; Finite fields; Mattila–Sjölin type functions | 公開日期: | 2021 | 來源出版物: | Vietnam Journal of Mathematics | 摘要: | Let ϕ(x, y) : ℝd× ℝd→ ℝ be a function. We say ϕ is a Mattila–Sjölin type function of index γ if γ is the smallest number satisfying the property that for any compact set E⊂ ℝd, ϕ(E,E) has a non-empty interior whenever dimH(E) > γ. The usual distance function, ϕ(x,y) = |x − y|, is conjectured to be a Mattila–Sjölin type function of index d2. In the setting of finite fields Fq, this definition is equivalent to the statement that ϕ(E, E) = Fq whenever |E|≫ qγ. The main purpose of this paper is to prove the existence of such functions with index d2 in the vector space Fqd. © 2021, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85118666861&doi=10.1007%2fs10013-021-00538-z&partnerID=40&md5=620bbf6f818bf4dce41fee7ddc4ac09d https://scholars.lib.ntu.edu.tw/handle/123456789/624587 |
ISSN: | 2305221X | DOI: | 10.1007/s10013-021-00538-z |
顯示於: | 數學系 |
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