Results on the Erdos-Falconer distance problem in Zqd for odd q

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:426

Article

Covert, David J.

关键词: Erdos-Falconer distance problem;    Discrete mathematics;    Geometric combinatorics;   

DOI  :  10.1016/j.jmaa.2015.01.063

来源: Elsevier

【 摘 要 】

The Eras Falconer distance problem in Z(q)(d) asks one to show that if E subset of Z(q)(d) is of sufficiently large cardinality, then the set of distances determined by E satisfies Delta(E) = Z(q). Previous results were known only in the case q = p(e), where p is an odd prime, and as such only showed that all units were obtained in the distance set. We give the first such result over rings Z(q), where q is no longer confined to be a prime power, and despite this, we show that the distance set of E contains all of Z(q), whenever E is of sufficiently large cardinality. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free