A note on diophantine approximation
A note on diophantine approximation
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关于丢番图近似的注记
DOI：
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发表时间：
1972
影响因子：
0.7
通讯作者：
K. C. Prasad
中科院分区：
文献类型：
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作者：
M. Prasad;K. C. Prasad
其中<；xn表示[0，An，...，Flj+̂+i，An+2，...]和pjqn=[0，au…，an~]，第n次收敛到；特别地，pjqt=L/a^(V)两个无理数^x和Gb是等价的(例如^t~^2)，如果它们的简单连分式从某一点开始符合。在(3)中，给出了与马氏(1)的定理链相对应的至少m个逼近的定理链。如果允许m-gt；co，则前者的定理就变成了后者的定理。在本文中，我们以不同的方式讨论了前链的第三个定理(即这里的定理1)。按照(3)中的技巧，我们首先给出一个引理，并在此引理的基础上恢复定理1，得到另一个逼近定理。我们现在陈述所有这些结果。
where <xn denotes [0, an, ..., flJ + ̂ + i , an+2, ...] and pjqn = [0, au ..., an~], the nth convergent to <!;; in particular pjqt = l/a^ (v) Two irrational numbers ^x and £2 are equivalent (e.g. ^t~^2) if their simple continued fractions tally from some point on. In (3), the chain of theorems for at least m approximations corresponding to the chain of theorems of Markov (1) is given. Theorems of the former chain becomes those of the latter if one allows m->co. In this paper, we discuss the third theorem of the former chain (namely Theorem 1 here) in a different manner. Following a technique of (3) we work out a lemma first and, on the basis of this lemma, we recover Theorem 1 and obtain another approximation theorem also. We now state all these results.