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

页码：1182 / 1194

页数：13

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