The absolute continuity of a limit law for Sylvester series
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 distribution of real-valued Q-additive functions modulo 1
The joint distribution of the binary digits of integer multiples
The measure of non-normal sets.
The metrical theory of continued fractions to the nearer integer
The Number of Steps in a Finite Jacobi Algorithm.
The Zeckendorf expansion of polynomial sequences
In the first part of the paper we prove that the Zeckendorf sum-of-digits function and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the -ary expansions of integers are asymptotically independent.
Transformations that preserve uniform distribution
Types de répartition complète des suites