On a thin set of integers involving the largest prime factor function.
On an additive property of squares and primes
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 certain solutions of the diophantine equation x-y = p(z)
On completely dense sequences
On difference sets of sets of integers
On difference sets of sets of positive integers
On gaps in Rényi -expansions of unity for an algebraic number
Let be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi -expansion of unity which controls the set of -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in are shown to exhibit a “gappiness” asymptotically bounded above by , where is the Mahler measure of . The proof of this result provides in a natural way a new classification of algebraic numbers with classes called Q...
On limit points of subsequences of uniformly distributed sequences
Given a subsequence of a uniformly distributed sequence, relations between the asymptotic densities of sets of its indices and the Lebesgue measure of the set of all its limit points are studied.
On ratio sets of natural numbers
On relations between -density and -density
In this paper it is discus a relation between -density and -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.
On relatively prime subsets and supersets.
On sequences of positive integers
On sets of natural numbers without solution to a noninvariant linear equation
On similarity between topologies
Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
On some properties of dispersion of block sequences of positive integers
On subseries.
On Subseries of Divergent Series
On sum-sets and product-sets of complex numbers
We give a simple argument that for any finite set of complex numbers , the size of the the sum-set, , or the product-set, , is always large.
On the class of all reciprocal bases for integers.