Approximating reals by sums of rationals

JOURNAL OF NUMBER THEORY

卷:129

Article

Chan, Tsz Ho

关键词: Diophantine approximation;    Exponential sum;    Erdos-Turan inequality;    Smooth number;   

DOI  :  10.1016/j.jnt.2008.08.005

来源: Elsevier

【 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.

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