https://scholars.lib.ntu.edu.tw/handle/123456789/624586
標題: | A sharp exponent on sum of distance sets over finite fields | 作者: | Koh D Pham T CHUN-YEN SHEN Vinh L.A. |
公開日期: | 2021 | 卷: | 297 | 期: | 44624 | 起(迄)頁: | 1749-1765 | 來源出版物: | Mathematische Zeitschrift | 摘要: | We study a variant of the Erdős–Falconer distance problem in the setting of finite fields. More precisely, let E and F be sets in Fqd, and Δ (E) , Δ (F) be corresponding distance sets. We prove that if |E F|≥Cqd+13 for a sufficiently large constant C, then the set Δ (E) + Δ (F) covers at least a half of all distances. Our result in odd dimensional spaces is sharp up to a constant factor. When E lies on a sphere in Fqd, it is shown that the exponent d+13 can be improved to d-16. Finally, we prove a weak version of the Erdős–Falconer distance conjecture in four-dimensional vector spaces for multiplicative subgroups over prime fields. The novelty in our method is a connection with additive energy bounds of sets on spheres or paraboloids. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087316551&doi=10.1007%2fs00209-020-02578-6&partnerID=40&md5=d8688939b077dc5d82afc2df78b5c708 https://scholars.lib.ntu.edu.tw/handle/123456789/624586 |
ISSN: | 00255874 | DOI: | 10.1007/s00209-020-02578-6 |
顯示於: | 數學系 |
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