Limit theorems for lacunary series and uniform distribution mod 1
Limit Theorems for Sums of Partial Quotients of Continued Fractions.
Limit theorems for the Matsumoto zeta-function
In this paper two weighted functional limit theorems for the function introduced by K. Matsumoto are proved.
Limit theorems for the Mellin transform of the square of the Riemann zeta-function. I
Limit theorems for uniformly distributed p-adic sequences
Limiting curlicue measures for theta sums
We consider the ensemble of curves {γα, N: α∈(0, 1], N∈ℕ} obtained by linearly interpolating the values of the normalized theta sum N−1/2∑n=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...
Limiting distributions and mean-values of multiplicative arithmetical functions.
Linear discrepancy of basic totally unimodular matrices.
Linear mod one transformations and the distribution of fractional parts {ξ(p/q)ⁿ}
Lineare Gleichverteilung.
Lineare Gleichverteilung.
Localised value-distribution of additive arithmetic functions.
Lois de répartition des diviseurs.
Lois de répartition des diviseurs
Lois de répartition des diviseurs, 2
Lois de répartition des diviseurs, 3
Lois de répartition des diviseurs. IV
Soit un sous-intervalle de ; on montre que la probabilité pour qu’un diviseur d’un entier appartiennent à possède une loi de distribution dont la mesure de répartition est atomique, à support inclus dans l’ensemble des nombres dyadiques.
Low-Discrepancy Point Sets.
Low-discrepancy point sets for non-uniform measures
We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on there exists a point set whose star-discrepancy with respect to μ is of order . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...
Low-discrepancy point sets obtained by digital constructions over finite fields