Some metrical theorems in diophantine approximation
Some metrical theorems in diophantine approximation
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DOI：
10.1017/s0305004100026323
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发表时间：
1950-04
影响因子：
0.8
通讯作者：
J. Cassels
中科院分区：
文献类型：
--
作者：
J. Cassels
导论.如果θ n是一个真实的数，我们用θ n表示θ n和最近的整数之间的差，即众所周知（例如Koksma（3），I，Satz 4），如果θ1，θ2，.，θn是任何真实的数，不等式有无穷多个整数解q > 0。特别地，如果α是任何真实的数，则该不等式有无穷多个解。
Introduction. If ξ is a real number we denote by ∥ ξ ∥ the difference between ξ and the nearest integer, i.e. It is well known (e.g. Koksma (3), I, Satz 4) that if θ1, θ2, …, θn are any real numbers, the inequality has infinitely many integer solutions q > 0. In particular, if α is any real number, the inequality has infinitely many solutions.