Metrical theorems on fractional parts of sequences
Metrical theorems on fractional parts of sequences
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DOI：
10.1090/s0002-9947-1964-0159802-4
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发表时间：
1964-03
影响因子：
1.3
通讯作者：
W. Schmidt
中科院分区：
文献类型：
--
作者：
W. Schmidt
1.导论.设C是模1的真实的数的加法群，x-+{x}是实数到C的自然映射.很清楚我们所说的C中的区间I和I的长度l（I）是什么意思。将真实的数a到最接近的整数的距离表示为|OC 11. C中实数集4的图像满足||-? 11<？给定0和0< e< 1/2是长度为2 e的C的区间的示例。
1. Introduction. Let C be the additive group of real numbers modulo 1, and let x-+{x} be the natural mapping from the reals onto C. It is clear what we shall mean by an interval I in C and by the length l (I) of I. Denote the distance of the real number a to the closest integer by| oc 11. The image in C of the set of reals 4 satisfying||-? 11<? with given 0 and 0< e< 1/2 is an example of an interval of C of length 2e.