Probabilistic Constructions of B_2[g] Sequences  

作　　者：Javier CILLERUELO 

机构地区：[1]Instituto de Ciencias Matermáticas(CSIC-UAM-UCM) [2]Department of Mathematics,Universidad Autónoma de Madrid

出　　处：《Acta Mathematica Sinica,English Series》2010年第7期1309-1314,共6页数学学报（英文版）

基　　金：Supported by project MTM 2008-03880 of MICINN (Spain) ;by the joint Madrid Region-UAM project TENU3 (CCG08-UAM/ESP-3906)

摘　　要：We use the probabilistic method to prove that for any positive integer g there exists an infinite B2[g] sequence A = {ak} such that ak ≤ k^2＋1/g（log k）^1/g＋0（1） as k→∞. The exponent 2＋1/g improves the previous one, 2 ＋ 2/g, obtained by Erdos and Renyi in 1960. We obtain a similar result for B2 [g] sequences of squares.We use the probabilistic method to prove that for any positive integer g there exists an infinite B2[g] sequence A = {ak} such that ak ≤ k^2＋1/g（log k）^1/g＋0（1） as k→∞. The exponent 2＋1/g improves the previous one, 2 ＋ 2/g, obtained by Erdos and Renyi in 1960. We obtain a similar result for B2 [g] sequences of squares.

关 键 词：Sidon sets B2 [g] sequences probabilistic method 

分 类 号：O212[理学—概率论与数理统计]