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

Youssef Lazar

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
4 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)200-217
Number of pages18
JournalJournal of Number Theory
Volume181
Early online date18 Jul 2017
DOIs
Publication statusPublished - Dec 2017

Keywords

  • Quadratic forms
  • Diophantine approximation
  • Algebraic groups
  • Strong approximation
  • Ratner's Orbit Closure Theorem

Cite this