Dani, S. G. ; Nogueira, Arnaldo
(2002)
*On orbits of sl(2, _{z} )+ and values of binary quadratic forms on positive integral pairs*
Journal of Number Theory, 95
(2).
pp. 313-328.
ISSN 0022-314X

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Official URL: http://dx.doi.org/10.1006/jnth.2001.2761

Related URL: http://dx.doi.org/10.1006/jnth.2001.2761

## Abstract

We consider actions of SL(2, Z) and SL(2, Z)+ (semigroup of matrices with nonnegative integral entries) on the projective space P and on P×P. Results are obtained on orbit-closures under these actions and they are applied to describe a class of binary quadratic forms Q such that the sets Q(Z ^{2}) or Q(Z +^{2}) are dense in R. We prove also a result generalising a theorem of Troessaert and Valette (On values at integer points of some irrational quadratic forms, preprint) associating to certain binary quadratic forms Q rational quadratic forms Q' such that the closure of Q(Z ^{2}) contains Q'(Z ^{2}).

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 8252 |

Deposited On: | 26 Oct 2010 12:00 |

Last Modified: | 30 May 2011 06:00 |

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