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

页码：316 / 324

页数：9