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Displaying similar documents to “On some vector balancing problems”

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 | 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 sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

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We have K - G k j K + G α j H j 3 ( 1 2 ) ϵ G K 1 + ϵ for K ϵ G 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 + 1 4 to which the Hecke series H j ( s ) is attached. This result yields the new bound H j ( 1 2 ϵ k j 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 = ( - D ) be an imaginary quadratic field, and denote by h its class number. It is shown that there is an absolute constant c &gt; 0 such that for sufficiently large D at least c · h 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 1 p N - log 1 p N - ψ ( N ) (for p q ) where ψ ( N ) tends to + . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case p = q = 1 2 .