✦ LIBER ✦
On Orbits of SL(2,Z)+ and Values of Binary Quadratic Forms on Positive Integral Pairs
✍ Scribed by S.G. Dani; Arnaldo Nogueira
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 183 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
We consider actions of SLð2; ZÞ and SLð2; ZÞ þ (semigroup of matrices with nonnegative integral entries) on the projective space P and on P Â 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 QðZ 2 Þ or QðZ 2 þ Þ 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 0 such that the closure of QðZ 2 Þ contains Q 0 ðZ 2 Þ.