On distribution functions of ξ(3/2)ⁿ mod 1

Strauch, Oto

doi:10.4064/aa-81-1-25-35

Cited by 8 publications

(10 citation statements)

References 6 publications

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“…Indeed, if we consider any function We now pose a question related to a conjecture of Strauch [10], which says that every measurable set X ⊂ [0, 1] having measure at least 2/3 is a set of uniqueness of any distribution function of {ξ (3/2) We note that the above result as well as our Theorem 1 include the case p = 3, q = 2. However, when q ≥ 3, the cases where we assume that p ≥ q(q − 1) in Theorem 1 are mutually exclusive from those considered in the above statement which requires p < 2q.…”

Section: Remarksmentioning

confidence: 99%

“…As an application of this result, Strauch showed (see Section 5 of [10]) that the distribution function g given by…”

mentioning

confidence: 91%

“…In other words, if g 1 and g 2 are any two distribution functions of the sequence which agree on X, then they agree on [0, 1]. Strauch [10] proved the following theorem.…”

mentioning

confidence: 99%

“…The questions taken up in this paper are mainly motivated by a paper of Strauch [10]. We refer to this paper for statements of several related conjectures and some results of Choquet [2] and Tijdeman [11] in those directions.…”

mentioning

confidence: 99%

“…In [10], Strauch studied distribution functions of {ξ(3/2) n }. For a distribution function g of a given sequence, we call a set X ⊂ [0, 1] a set of uniqueness of g if defining g on X uniquely determines it in all of [0,1].…”

mentioning

confidence: 99%

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On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}

2005

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Section: Remarksmentioning

confidence: 99%

“…As an application of this result, Strauch showed (see Section 5 of [10]) that the distribution function g given by…”

mentioning

confidence: 91%

“…In other words, if g 1 and g 2 are any two distribution functions of the sequence which agree on X, then they agree on [0, 1]. Strauch [10] proved the following theorem.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}

2005

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Quantitative uniform distribution results for geometric progressions

Aistleitner

2014

Isr. J. Math.

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By a classical theorem of Koksma the sequence of fractional parts ({x n }) n≥1 is uniformly distributed for almost all values of x > 1. In the present paper we obtain an exact quantitative version of Koksma's theorem, by calculating the precise asymptotic order of the discrepancy of ({ξx sn }) n≥1 for typical values of x (in the sense of Lebesgue measure). Here ξ > 0 is an arbitrary constant, and (s n ) n≥1 can be any increasing sequence of positive integers.

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On a sequence related to that of Thue–Morse and its applications

Dubickas

2007

Discrete Mathematics

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It is known that the sequence 1, of lengths of blocks of identical symbols in the Thue-Morse sequence has several extremal properties among all non-periodic sequences of the symbols 1 and 2. Its generatingIn terms of combinatorics on words, for any given x ∈ (0, 1) and > 0, we prove that every non-periodic word of an alphabet {1, 2} has a suffix s whose generating function S(x) satisfies the inequality xS(−x) > 1−W (−x)− . Using this, we prove several bounds for the largest and the smallest limit points of the sequence of fractional parts { b n }, n = 0, 1, 2, . . ., where b < − 1 is a negative rational number and is a real number. Our results show, for example, that, for any real number = 0, the sequence of fractional parts { (−3/2) n }, n = 0, 1, 2, . . ., has a limit point greater than 0.466452. Furthermore, for each integer b −2 and each real number / ∈ Q, we prove that lim inf n→∞ { b n } ∞ k=1 (1−|b| −(2 k +(−1) k−1 )/3 ) and show that this inequality is sharp.

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On distribution functions of ξ(3/2)ⁿ mod 1

Cited by 8 publications

References 6 publications

On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}

On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}

Quantitative uniform distribution results for geometric progressions

On a sequence related to that of Thue–Morse and its applications

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On distribution functions of ξ(3/2)ⁿ mod 1

Cited by 8 publications

References 6 publications

On the sets of uniqueness of a distribution function of {ξ(p/q)n}

On the sets of uniqueness of a distribution function of {ξ(p/q)n}

Quantitative uniform distribution results for geometric progressions

On a sequence related to that of Thue–Morse and its applications

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Product

Resources

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On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}

On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}