On orbits of SL(2,Z)+ and values of binary quadratic forms on positive integral pairs

[摘要] 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 x 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)). (C) 2002 Elsevier Science (USA).

[发布日期] 2002-08-01