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引用次数: 2
摘要
K. Mahler猜想:对于所有n = 0,1,2，…，不存在ξ∈v +使得分数部分{ξ(3/2)n}满足0≤{ξ(3/2)n} < 1/2这样的ξ，如果存在，就叫做马勒z数。本文证明了如果ξ是z数，则序列xn = {ξ(3/2)n}， n = 1,2，…有渐近分布函数c0(x)，其中对于x∈(0,1)，c0(x)=1。
Abstract K. Mahler’s conjecture: There exists no ξ ∈ ℝ+ such that the fractional parts {ξ(3/2)n} satisfy 0 ≤ {ξ(3/2)n} < 1/2 for all n = 0, 1, 2,... Such a ξ, if exists, is called a Mahler’s Z-number. In this paper we prove that if ξ is a Z-number, then the sequence xn = {ξ(3/2)n}, n =1, 2,... has asymptotic distribution function c0(x), where c0(x)=1 for x ∈ (0, 1].
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