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Values of pairs involving one quadratic form and one linear form at S-integral points
Journal article   Peer reviewed

Values of pairs involving one quadratic form and one linear form at S-integral points

Youssef Lazar
Journal of number theory, Vol.181, pp.200-217
12/2017
DOI: https://doi.org/10.1016/j.jnt.2017.06.003

Abstract

Algebraic groups Diophantine approximation Quadratic forms Ratner's orbit closure theorem Strong approximation
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.

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