Corrigendum to the paper "Limit theorems for the Mellin transform of the square of the Riemann zeta-function. I" (Acta Arith. 122 (2006), 173-184)
Corrigendum to the paper "On the distribution of s-dimensional Kronecker sequences" Acta Arith. 51 (1988), 335-347
Corrigendum to Theorem 5 of the paper "Asymptotic density of A ⊂ ℕ and density of the ratio set R(A) (Acta Arith. 87 (1998), 67-78)
Counting rational points near planar curves
We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².
Courants ergodiques et répartition géométrique.
Critères d'équirépartition modulo un
Criterion for uniform distribution of sequences and a class of Riemann integrable functions
Das Gesetz vom iterierten Logarithmus mit Anwendungen auf die Zahlentheorie.
Das Hausdorff-Maß von Cantormengen.
Das Wienersche Maß einer gewissen Menge von Vektorfunktionen.
D-Dimensional Hypercubes and the Euler and MacNeish Conjectures.
De nouveaux curieux produits infinis
Définition de paramètres d'équirépartition
Démonstration d'une conjecture de P. Erdös
Density modulo 1 in local fields
Density of some sequences modulo 1
Recently, Cilleruelo, Kumchev, Luca, Rué and Shparlinski proved that for each integer a ≥ 2 the sequence of fractional parts is everywhere dense in the interval [0,1]. We prove a similar result for all Pisot numbers and Salem numbers α and show that for each c > 0 and each sufficiently large N, every subinterval of [0,1] of length contains at least one fractional part Q(αⁿ)/n, where Q is a nonconstant polynomial in ℤ[z] and n is an integer satisfying 1 ≤ n ≤ N.
Der Differenzensatz von van der Corput und gleichverteilte Funktionen.
Der individuelle Ergodensatz in der Theorie der Gleichverteilung mod 1.
Des mots en arithmétique
Développement en base , répartition modulo un de la suite , n, langages codés et -shift