1. CMB 2011 (vol 56 pp. 161)
|An Extension of the Dirichlet Density for Sets of Gaussian Integers|
Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of density to higher dimensional sets of integers. In this work, we propose an extension of the Dirichlet density for sets of Gaussian integers and investigate some of its properties.
Keywords:Gaussian integers, Dirichlet density
Categories:11B05, 11M99, 11N99
2. CMB 1999 (vol 42 pp. 441)
|Product Bases for the Rationals |
A sequence of positive rationals generates a subgroup of finite index in the multiplicative positive rationals, and group product representations by the sequence need only a bounded number of terms, if and only if certain related sequences have densities uniformly bounded from below.