Article
MAHLER’S CONJECTURE ON ξ(3/2)n mod 1
Authors
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].
Keywords
distribution function, fractional part, Z-number.
Citation
Strauch, O. (2021). MAHLER’S CONJECTURE ON ξ(3/2)n mod 1. Uniform Distribution Theory, 16(2), 49–70. https://doi.org/10.2478/UDT-2021-0007
O. Strauch, “MAHLER’S CONJECTURE ON ξ(3/2)n mod 1,” Uniform Distribution Theory, vol. 16, no. 2, pp. 49–70, 2021, doi: 10.2478/UDT-2021-0007.
Strauch O. MAHLER’S CONJECTURE ON ξ(3/2)n mod 1. Uniform Distribution Theory. 2021;16(2):49–70. doi:10.2478/UDT-2021-0007.
Strauch, O. (2021), ‘MAHLER’S CONJECTURE ON ξ(3/2)n mod 1’, Uniform Distribution Theory, 16(2), pp. 49–70. Available at: https://doi.org/10.2478/UDT-2021-0007.
Strauch, Oto. “MAHLER’S CONJECTURE ON ξ(3/2)n Mod 1.” Uniform Distribution Theory, vol. 16, no. 2, 2021, pp. 49–70. https://doi.org/10.2478/UDT-2021-0007.
Strauch, Oto. “MAHLER’S CONJECTURE ON ξ(3/2)n Mod 1.” Uniform Distribution Theory 16, no. 2 (2021): 49–70. https://doi.org/10.2478/UDT-2021-0007.
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Published by: Engineering Journals
