Atkin's theorem on pseudo-squares.
Buck's measure density and sets of positive integers containing arithmetic progression
Congruent subsets of infinite sets of natural numbers.
Connections between connected topological spaces on the set of positive integers
In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of...
Convergence of subseries of the harmonic series and asymptotic densities of sets of positive integers.
Corrigendum to the paper "On ratio sets of sets of natural numbers"
Corrigendum to Theorem 5 of the paper "Asymptotic density of A ⊂ ℕ and density of the ratio set R(A) (Acta Arith. 87 (1998), 67-78)
Counting monic irreducible polynomials in for which order of is odd
Hasse showed the existence and computed the Dirichlet density of the set of primes for which the order of is odd; it is . Here we mimic successfully Hasse’s method to compute the density of monic irreducibles in for which the order of is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the ’s as varies through all rational primes.
Covering densities
Densités, moyennes et ensemble représentatif : unification du cas discret et du cas continu
Densities in disjoint unions
Density inequalities for a restricted sum of sets of lattice points
Density of M-sets in arithmetic progression
Dispersion of ratio block sequences and asymptotic density
Distance sets, ratio sets and certain transformations of sets of real numbers
Distribution Preserving Sequences of Maps and Almost Constant Sequences on Finite Sets.
Einige neuere Untersuchungen über die Dichte in der additiven Zahlentheorie.
Errata to the paper: ``Remarks on maximum and minimum exponents in factoring'
Gaps between consecutive divisors of factorials
The set of all divisors of , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest and obtain a lower bound on their distance.
Gaps between primes in Beatty sequences
We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).