Approximating reals by sums of two rationals

被引：4
|
作者：
Chan, Tsz Ho [1 ]
机构：
[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
来源：
JOURNAL OF NUMBER THEORY | 2008年 / 128卷 / 05期
关键词：
Diophantine approximation; character sum; exponential sum; Erdos-Turan inequality;
D O I：
10.1016/j.jnt.2007.06.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We generalize Dirichlet's diophantine approximation theorem to approximating any real number alpha by a sum of two rational numbers a(1)/q(1) + a(2)/q(2) with denominators 1 <= q(1), q(2) <= N. This turns out to be related to the congruence equation problem xy =c (mod q) with 1 <= x, y <= q(1/2+is an element of). (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：1182 / 1194
页数：13
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