Uniform distribution of sequences
Uniform distribution of sequences
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发表时间：
1974
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通讯作者：
L. Kuipers
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作者：
L. Kuipers
(1)如果(2)Lim(1/N)A(x，N，{xn}z)-x(0x0)，则(X)对几乎所有的t(H.Davenport和P.ErdSs[2])都是均匀分布的modz。在下文中，我们用初等方法证明了其中一些结果的推广。[7]))。为此，我们定义了一个几乎均匀分布的序列(X)，如果存在一个无限序列N<；N<；……满足(3)LIM(1/N)A(x，N，{x})=x(0x-lt；L)的正整数
( 1 ) {xn}z= Xn--Z_I Zin-Ztn-I is uniformly distributed mod 1, i.e., if ( 2 ) lim (1/N)A(x, N, {xn}z)-x (0x0), then (x) is uniformly distributed modz for almost all t (H. Davenport and P. ErdSs [2]). In the following we prove a generalization of some of these results by an elementary method (cf. [7]). For this purpose we define a sequence (x) to be almost uniformly distributed mod z if there is an infinite sequence N<N<... of positive integers such that ( 3 ) lim (1/N)A(x, N, {x})= x (0x-<l)