Rational criterion testing the density of additive subgroups of R^n and C^n

Mohamed Elghaoui

Tunisia

University of Carthage

Faculty of Sciences of Bizerte 7021 Jarzouna, Bizerte

Department of Mathematics

Adlene Ayadi

Tunisia

University of Gafsa

Faculty of sciences

Submitted: 2014-09-05

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Accepted: 2015-07-27

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Published: 2015-10-01

DOI: https://doi.org/10.4995/agt.2015.3257
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Keywords:

dense, additive group, rationally independent, Kronecker.

Supporting agencies:

This research was not funded

Abstract:

In this paper, we give an explicit criterion to decide the
density of finitely generated additive subgroups of R^n and C^n.

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References:

A. Ayadi and H. Marzougui, Dense orbits for abelian subgroups of GL(n, $mathbb{C$), Foliations 2005, World Scientific, Hackensack, NJ, (2006), 47-69.

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http://dx.doi.org/10.1080/10236198.2011.582466

A. Ayadi, Hypercyclic abelian groups of affine maps on $mathbb{C}^{n}$, Canad. Math. Bull. 56 (2013), 477-490.

http://dx.doi.org/10.4153/CMB-2012-019-6

N. S. Feldman, Hypercyclic tuples of operators and somewhere dense orbits, J. Math. Anal. Appl. 346 (2008), 82-98.

http://dx.doi.org/10.1016/j.jmaa.2008.04.027

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960.

L. Kronecker, Nherungsweise ganzzahlige Auflsung linearer Gleichungen, Monatsberichte Knigl. Preu. Akad. Wiss. Berlin, (1884), 1179-1193 and 1271-1299.

M. Waldschmidt,Topologie des points rationnels, Cours de troisi`eme Cycle, Universit'e P. et M. Curie (Paris VI), (1994/95).

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