Sur certaines suites uniformément équiréparties modulo 1
Sur des nombres normaux définis par un polynôme
Sur les décimales des nombres algébriques réels
Sur les fonctions q-additives ou q-multiplicatives
Sur les fractions continues limitées
Sur un procédé particulier de division rapide
Symmetric CNS trinomials.
Terminating cycles for iterated difference values of five digit integers.
The complex sum of digits function and primes
Canonical number systems in the ring of gaussian integers are the natural generalization of ordinary -adic number systems to . It turns out, that each gaussian integer has a unique representation with respect to the powers of a certain base number . In this paper we investigate the sum of digits function of such number systems. First we prove a theorem on the sum of digits of numbers, that are not divisible by the -th power of a prime. Furthermore, we establish an Erdös-Kac type theorem...
The determination of all four-digit Kaprekar constants.
The digits of 1/p in connection with class number factors
The distribution of the sum-of-digits function
By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.
The factorial representations of integers and the Eratosthenes sieve
The general quasi-order algorithm in number theory.
The geometry of non-unit Pisot substitutions
It is known that with a non-unit Pisot substitution one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional realization...
The joint distribution of q-additive functions
The joint distribution of the binary digits of integer multiples
The Length of Periodic Continued Fractions.
The number of binomial coefficients in residue classes modulo p and .
The p-adic valuation of k-central binomial coefficients