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 2009 (vol 53 pp. 204)
|Corrigendum for "Consecutive large gaps in sequences defined by multiplicative constraints"|
3. CMB 2008 (vol 51 pp. 172)
|Consecutive Large Gaps in Sequences Defined by Multiplicative Constraints |
In this paper we obtain quantitative results on the occurrence of consecutive large gaps between $B$-free numbers, and consecutive large gaps between nonzero Fourier coefficients of a class of newforms without complex multiplication.
Keywords:$B$-free numbers, consecutive gaps
4. CMB 2001 (vol 44 pp. 12)
|A Technique of Studying Sums of Central Cantor Sets |
This paper is concerned with the structure of the arithmetic sum of a finite number of central Cantor sets. The technique used to study this consists of a duality between central Cantor sets and sets of subsums of certain infinite series. One consequence is that the sum of a finite number of central Cantor sets is one of the following: a finite union of closed intervals, homeomorphic to the Cantor ternary set or an $M$-Cantorval.