Approximating reals by sums of rationals

被引：2
|
作者：
Chan, Tsz Ho [1 ]
机构：
[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
来源：
JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 02期
关键词：
Diophantine approximation; Exponential sum; Erdos-Turan inequality; Smooth number;
D O I：
10.1016/j.jnt.2008.08.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the question of approximating any real number a by sums of n rational numbers a(1)/q(1) + a(2)/q(2) + ... + a(n)/q(n) with denominators 1 <= q(1), q(2), ..., q(n) <= N. This leads to inquiries on approximating a real number by rational numbers with a prescribed number of prime factors in the denominator as well as by rational numbers with smooth denominator. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：316 / 324
页数：9
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