A Second Note on a Result of Haddad and Helou  

作　　者：Yujie WANG 

机构地区：[1]School of Mathematics and Computer Science, Anhui Normal University

出　　处：《Journal of Mathematical Research with Applications》2016年第3期272-274,共3页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11471017)

摘　　要：Let K be a finite field of characteristic ≠ 2 and G the additive group of K × K. Let k_1, k_2 be integers not divisible by the characteristic p of K with（k_1, k_2） = 1. In 2004, Haddad and Helou constructed an additive basis B of G for which the number of representations of g ∈ G as a sum b_1＋ b_2（b_1, b_2 ∈ B） is bounded by 18. For g ∈ G and B■G, let σk_1,k_2（B, g）be the number of solutions of g = k_1b_1 ＋ k_2b_2, where b_1, b_2 ∈ B. In this paper, we show that there exists a set B ？ G such that k_1 B ＋ k2 B = G and σk_1,k_2（B, g）≤16.Let K be a finite field of characteristic ≠ 2 and G the additive group of K × K. Let k_1, k_2 be integers not divisible by the characteristic p of K with（k_1, k_2） = 1. In 2004, Haddad and Helou constructed an additive basis B of G for which the number of representations of g ∈ G as a sum b_1＋ b_2（b_1, b_2 ∈ B） is bounded by 18. For g ∈ G and B■G, let σk_1,k_2（B, g）be the number of solutions of g = k_1b_1 ＋ k_2b_2, where b_1, b_2 ∈ B. In this paper, we show that there exists a set B ？ G such that k_1 B ＋ k2 B = G and σk_1,k_2（B, g）≤16.

关 键 词：integers additive conjecture subset subgroup proof multiplicative discriminant analogue instance 

分 类 号：O152[理学—数学]