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# An Extension of the Dirichlet Density for Sets of Gaussian Integers

Published:2011-08-03
Printed: Mar 2013
• L. C. Rêgo,
Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, PE, Brazil
• R. J. Cintra,
Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, PE, Brazil
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## Abstract

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
 MSC Classifications: 11B05 - Density, gaps, topology 11M99 - None of the above, but in this section 11N99 - None of the above, but in this section