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
Die Diskrepanz von Differenzenfolgen im p-adischen.
Die Hausdorff-Dimension von Mengen reeller Zahlenfolgen.
Digital expansion of exponential sequences
We consider the -ary digital expansion of the first terms of an exponential sequence . Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first digits, where is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo ...
Digital Nets and Sequences Constructed over Finite Rings and Their Application to Quasi-Monte Carlo Integration.
Digital sum moments and substitutions
Digital (t,m,s)-nets and the spectral test
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...