On a series of cosecants related to a problem in ergodic theory
On a theorem of Daboussi related to the set of Gaussian integers.
On a theorem of V. Bernik in the metric theory of Diophantine approximation
On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
On additive functions
On additive functions having a non-decreasing normal order
On additive functions with a non-decreasing normal order
On almost even arithmetical functions via orthonormal systems on Vilenkin groups
On an application of uniform distribution of sequences
On an inequality for additive arithmetic functions
On approximation by Lüroth series
Let and be its sequence of Lüroth Series convergents. Define the approximation coefficients by . In [BBDK] the limiting distribution of the sequence was obtained for a.e. using the natural extension of the ergodic system underlying the Lüroth Series expansion. Here we show that this can be done without the natural extension. In fact we will prove that for each is already distributed according to the limiting distribution. Using the natural extension we will study the distribution for...
On asymptotic density and uniformly distributed sequences
Assuming Martin's axiom we show that if X is a dyadic space of weight at most continuum then every Radon measure on X admits a uniformly distributed sequence. This answers a problem posed by Mercourakis [10]. Our proof is based on an auxiliary result concerning finitely additive measures on ω and asymptotic density.
On asymptotically correlated -multiplicative functions.
On certain asymptotic functional equations.
On certain solutions of the diophantine equation x-y = p(z)
On certain statistical properties of continued fractions with even and with odd partial quotients
On completely dense sequences
On consecutive Farey arcs
On decimal and continued fraction expansions of a real number
On Dispersion and Markov Constants.