The relative size of consecutive odd denominators in Farey series.
The representation of real numbers by infinite series of rationals
The “Riemann hypothesis” for the Hawkins random Sieve
The role of functional equations in stochastic model building.
The sequences of prime divisors of integers
The structure of higher-dimensional noncommutative tori and metric diophantine approximation.
The theory of asymptotic distribution modulo one
The three-dimensional Gauss algorithm is strongly convergent almost everywhere.
The Turán-Kubilius inequality for integers free of large prime factors (II)
The Turán-Kubilius inequality for integers without large prime factors.
The universality of zeta-functions attached to certain cusp forms
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.
Théorème de Koksma en -adique
Théorèmes métriques sur les fractions continues
Tijdeman's Iterative Algorithm
Topological properties of two-dimensional number systems
In the two dimensional real vector space one can define analogs of the well-known -adic number systems. In these number systems a matrix plays the role of the base number . In the present paper we study the so-called fundamental domain of such number systems. This is the set of all elements of having zero integer part in their “-adic” representation. It was proved by Kátai and Környei, that is a compact set and certain translates of it form a tiling of the . We construct points, where...
Transformations preserving the Hausdorff-Besicovitch dimension
Continuous transformations preserving the Hausdorff-Besicovitch dimension (“DP-transformations”) of every subset of R 1 resp. [0, 1] are studied. A class of distribution functions of random variables with independent s-adic digits is analyzed. Necessary and sufficient conditions for dimension preservation under functions which are distribution functions of random variables with independent s-adic digits are found. In particular, it is proven that any strictly increasing absolutely continuous distribution...
Transformations that preserve uniform distribution
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Two binary additive problems.