Simultaneous rational approximations and related diophantine equations
Simultaneous rational approximations and related diophantine equations
复制标题
联立有理逼近和相关丢番图方程
DOI：
10.1017/s0305004100076118
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发表时间：
1993
影响因子：
0.8
通讯作者：
J. Rickert
中科院分区：
文献类型：
--
作者：
J. Rickert
在本文中，我们将考虑对有理T1，…形式的代数数的同时逼近，tm，V.if t1，…，tm关于一个公分母足够接近1，我们将得到一个有效的形式为max{|θ1-p1/q|，…，|θm-pm/q|}>；cq-1-λ适用于所有整数p1，…、PM、Q与Q>；0。我们用这个技巧来证明联立方程组的唯一解是平凡的解。
Abstract In this paper we shall consider simultaneous approximations to algebraic numbers of the form for rational t1, …, tm, v. If t1, …, tm, are sufficiently close to 1 with respect to a common denominator we shall derive an effective inequality of the form max {|θ1 – p1 / q|, …, |θm – pm / q|} > cq–1–λ for all integers p1, …, pm, q with q > 0. The technique is used to derive the inequality We use this to show that the only solution to the simultaneous equations are the trivial ones.