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...
Dimension de Hausdorff
Dimension de Hausdorff. Application aux nombres normaux
Dimension de Hausdorff de certains fractals aléatoires
On construit des ensembles de Cantor aléatoires par partages successifs de rectangles, en partant d’un carré, (le nombre de divisions de la longueur peut être différent de celui de la largeur). La construction est stationnaire : elle fait intervenir des variables aléatoires indépendantes et équidistribuées. Sur ces ensembles il existe une mesure naturelle, , aléatoire elle aussi. Des résultats concernant les boréliens portant et leur dimension de Hausdorff ont déjà été obtenus par J. Peyrière...
Dimension d'ensembles plans définis par des propriétés des développements des coordonnées
Dimension des courbes planes, papiers plies et suites de Rudin-Shapiro
Dimension of countable intersections of some sets arising in expansions in non-integer bases
We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.
Dimensions des spirales
Diophantine approximation, Hausdorff dimension and Schroder's functional equation
Diophantine Approximation in certain Solenoids
Diophantine approximation on affine hyperplanes
Diophantine Approximations of Infinite Series and Products
This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos' results on~irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.
Diophantine classes, dimension and Denjoy maps
Dirichlet series induced by the Riemann zeta-function
The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form for in . Among other things, using the Haar measure on for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.