On Oppenheim-type conjecture for systems of quadratic forms
| dc.creator | Gorodnik, Alexander | |
| dc.date | 2003-10-15 | |
| dc.date.accessioned | 2026-07-07T05:01:56Z | |
| dc.date.available | 2026-07-07T05:01:56Z | |
| dc.description | Let Q_i, i=1,...,t, be real nondegenerate indefinite quadratic forms in d variables. We investigate under what conditions the closure of the set {(Q_1(x),...,Q_t(x)): x\in Z^d-{0}} contains (0,..,0). As a corollary, we deduce several results on the magnitude of the set Δof g\in GL(d,R) such that the closure of the set {(Q_1(gx),...,Q_t(gx)): x\in Z^d-{0}} contains (0,...,0). Special cases are described when depending on the mutual position of the hypersurfaces {Q_i=0}, i=1,...,t, the set Δhas full Haar measure or measure zero and Hausdorff dimension d^2-(d-2)/2. | |
| dc.description | To be published in Israel Journal of Mathematics, 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310230 | |
| dc.identifier | http://arxiv.org/abs/math/0310230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68866 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Number Theory | |
| dc.subject | 37A17, 11J13, 11H55 | |
| dc.title | On Oppenheim-type conjecture for systems of quadratic forms | |
| dc.type | text |