A discrete Fourier kernel and Fraenkel's tiling conjecture
A generalization of Beatty's theorem.
A generalization of some results in additive number theory.
A mean value density theorem of additive number theory
A nontransformation proof of Mann's density theorem.
A note on the generalized 3n+1 problem
A note on uniform or Banach density
In this note we present and comment three equivalent definitions of the so called uniform or Banach density of a set of positive integers.
A notion of density and essential components in GF[p,x]
A problem of Rankin on sets without geometric progressions
A geometric progression of length k and integer ratio is a set of numbers of the form for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence of positive real numbers with a₁ = 1 such that the set contains no geometric progression of length k and integer ratio. Moreover, is a maximal subset of (0,1] that contains no geometric progression of length k and integer ratio. It is also proved that there is...
A short proof of a known density result.
A theorem of H. Steinhaus and -dense sets of positive integers
Abschätzung der Dichte von Summenmengen.
Additive properties of dense subsets of sifted sequences
We examine additive properties of dense subsets of sifted sequences, and in particular prove under very general assumptions that such a sequence is an additive asymptotic basis whose order is very well controlled.
Affine invariants, relatively prime sets, and a phi function for subsets of .
Aposyndesis in
We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic...
Arithmetic progressions of length three in subsets of a random set
Arithmetic progressions, prime numbers, and squarefree integers
In this paper we establish the distribution of prime numbers in a given arithmetic progression for which is squarefree.
Asymptotic densities of sets of positive integers
Asymptotic density of A⊂ ℕ and density of the ratio set R(A)
Atkin's theorem on pseudo-squares.