Mahler’s Conjecture on ξ(3/2)nmod 1
| Autor: | Strauch, Oto |
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| Zdroj: | Uniform Distribution Theory; December 2021, Vol. 16 Issue: 2 p49-70, 22p |
| Abstrakt: | 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 ξis 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]. |
| Databáze: | Supplemental Index |
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