Mahler’s Conjecture on ξ(3/2)nmod 1

Mahler’s Conjecture on ξ(3/2)nmod 1

K. Mahler’s conjecture: There exists no ∈ ℝ such that the fractional parts { (3/2) } satisfy 0 { (3/2) } < 1/2 for all = 0, 1, 2,... Such a , if exists, is called a Mahler’s -number. In this paper we prove that if is a -number, then the sequence = { (3/2) }, =1, 2,... has asymptotic distribution...

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Veröffentlicht in:Uniform distribution theory 2021-12, Vol.16 (2), p.49-70
1. Verfasser: Strauch, Oto
Format: Artikel
Sprache:eng
Schlagworte:
11J71
distribution function
fractional part
number
Primary: 11K06
Secondary: 11K31
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Zusammenfassung:K. Mahler’s conjecture: There exists no ∈ ℝ such that the fractional parts { (3/2) } satisfy 0 { (3/2) } < 1/2 for all = 0, 1, 2,... Such a , if exists, is called a Mahler’s -number. In this paper we prove that if is a -number, then the sequence = { (3/2) }, =1, 2,... has asymptotic distribution function ), where )=1 for ∈ (0, 1].
ISSN:2309-5377
DOI:10.2478/udt-2021-0007