On some vector balancing problems

Apostolos Giannopoulos

Displaying similar documents to “On some vector balancing problems”

On the sequence of numbers of the form $ε ₀ + ε ₁ q + . . . + ε_{n} q^{n}$ , $ε_{i} \in 0, 1$

Paul Erdős, István Joó, Vilmos Komornik (1998)

Acta Arithmetica

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Boundedness of Marcinkiewicz functions.

Minako Sakamoto, Kôzô Yabuta (1999)

Studia Mathematica

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The $L^{p}$ boundedness(1 < p < ∞) of Littlewood-Paley’s g-function, Lusin’s S function, Littlewood-Paley’s $g *_{λ}$ -functions, and the Marcinkiewicz function is well known. In a sense, one can regard the Marcinkiewicz function as a variant of Littlewood-Paley’s g-function. In this note, we treat counterparts $μ_{S}^{ϱ}$ and $μ_{λ}^{*, ϱ}$ to S and $g *_{λ}$ . The definition of $μ_{S}^{ϱ} (f)$ is as follows: $μ_{S}^{ϱ} (f) (x) = (ʃ_{| y - x | < t} | 1 / t^{ϱ} ʃ_{| z | \leq t} Ω (z) / {(| z |}^{n - ϱ} {) f (y - z) d z |}^{2} (d y d t) / (t^{n + 1}))^{1 / 2}$ , where Ω(x) is a homogeneous function of degree 0 and Lipschitz continuous of order β (0 < β ≤ 1) on the unit sphere $S^{n - 1}$ , and...

On the average number of direct factors of a finite Abelian group

Ekkehard Krätzel (1988)

Acta Arithmetica

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The moments of partitions, I

L. Richmond (1975)

Acta Arithmetica

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On sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

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We have $\sum_{K - G \leq k_{j} \leq K + G} α_{j} H_{j}^{3} (\frac{1}{2}) ≪_{ϵ} G K^{1 + ϵ}$ for $K^{ϵ} \leq G \leq K, where α_{j} = {|ρ_{j} (1)|}^{2} {(cosh π k_{j})}^{- 1}, and ρ_{j} (1)$ is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue $λ_{j} = k_{j}^{2} + \frac{1}{4}$ to which the Hecke series $H_{j} (s)$ is attached. This result yields the new bound $H_{j} (\frac{1}{2} ≪_{ϵ} k_{j}^{\frac{1}{3} + ϵ} .$

Statistical choice of non-separated one-parameter models.

José Tiago de Oliveira (1985)

Trabajos de Estadística e Investigación Operativa

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The purpose of this paper is to study the asymptotic choice between two models {F(x|α), α ∈ A ⊆ R} and {G(x|β), β ∈ B ⊆ R}, A and B being intervals but such that for (α, β}, and only for this pair, we have F(x|α) = G(x|β).

Non-vanishing of class group $L$ -functions at the central point

Valentin Blomer (2004)

Annales de l’institut Fourier

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Let $K = ℚ (\sqrt{- D})$ be an imaginary quadratic field, and denote by $h$ its class number. It is shown that there is an absolute constant $c > 0$ such that for sufficiently large $D$ at least $c \cdot h \prod_{p ∣ D} (1 - p^{- 1})$ of the $h$ distinct $L$ -functions $L_{K} (s, χ)$ do not vanish at the central point $s = 1 / 2$ .

Block distribution in random strings

Peter J. Grabner (1993)

Annales de l'institut Fourier

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For almost all infinite binary sequences of Bernoulli trials $(p, q)$ the frequency of blocks of length $k (N)$ in the first $N$ terms tends asymptotically to the probability of the blocks, if $k (N)$ increases like $\log_{\frac{1}{p}} N - \log_{\frac{1}{p}} N - ψ (N)$ (for $p \leq q$ ) where $ψ (N)$ tends to $+ \infty$ . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case $p = q = \frac{1}{2}$ .