We prove the existence of S -integral solutions of simultaneous diophantine inequalities for pairs (Q,L) involving one quadratic form and one linear form satisfying some arithmetico-geometric conditions. This result generalises previous results of Gorodnik and Borel-Prasad. The proof uses Ratner's theorem for unipotent actions on homogeneous spaces combined with an argument of strong approximation.
- Quadratic forms
- Diophantine approximation
- Algebraic groups
- Strong approximation
- Ratner's Orbit Closure Theorem