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Uniform Distribution Theory
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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 16. Issue 2


Published on

December, 2021


Pages

49-70


DOI

https://doi.org/10.2478/udt-2021-0007

Article

Mahler’s Conjecture on ξ(3/2)nmod 1


Authors

Oto Strauch


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].


Citation

Strauch, O. (2021). Mahler’s Conjecture on ξ(3/2)nmod 1. Uniform distribution theory, 16(2), 49-70. https://doi.org/10.2478/udt-2021-0007