Distance Sets Relating to Orthogonal Exponentials

作     者：Jian Lin LI 

作者机构：College of Mathematics and Information Science Shaanxi Normal University Xi＇an 710062 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第12期

页      面：2409-2414页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Key Project of Ministry of Education of China (Grant No. 108117) and National Natural Science Foundation of China (Grant No. 10871123) 

主　　题：Distance sets orthogonal exponentials convex sets algebraic number and transcendental number 

摘      要：The aim of this paper is to investigate the size properties of a planar set whose distance set has some prescribed arithmetic combinatorics. Such research is motivated by the conjecture that the disk has no more than 3 orthogonal exponentials. By proving a shifted version of ErdSs-Solymosi＇s theorem on the distance sets, we give some grounds on the conjecture. The results obtained here extend the corresponding results of Iosevich and Jaming in a simple manner.