Geodesic
An Extension of the Dirichlet Density for Sets of Gaussian Integers
Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 161-172

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DOI

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.
DOI : 10.4153/CMB-2011-149-9
Mots-clés : 11B05, 11M99, 11N99, Gaussian integers, Dirichlet density 
Rêgo, L. C.; Cintra, R. J. An Extension of the Dirichlet Density for Sets of Gaussian Integers. Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 161-172. doi: 10.4153/CMB-2011-149-9
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     author = {R\^ego, L. C. and Cintra, R. J.},
     title = {An {Extension} of the {Dirichlet} {Density} for {Sets} of {Gaussian} {Integers}},
     journal = {Canadian mathematical bulletin},
     pages = {161--172},
     year = {2013},
     volume = {56},
     number = {1},
     doi = {10.4153/CMB-2011-149-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-149-9/}
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