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

Youssef Lazar

doi:10.1016/j.jnt.2017.06.003

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

Youssef Lazar

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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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 language	English
Pages (from-to)	200-217
Number of pages	18
Journal	Journal of Number Theory
Volume	181
Early online date	18 Jul 2017
DOIs	https://doi.org/10.1016/j.jnt.2017.06.003
Publication status	Published - Dec 2017

Keywords

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

Access to Document

10.1016/j.jnt.2017.06.003

Accepted manuscriptAccepted author manuscript, 286 KBLicence: CC BY-NC-ND

http://linkinghub.elsevier.com/retrieve/pii/S0022314X17302305Licence: Unspecified

Cite this

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title = "Values of pairs involving one quadratic form and one linear form at S-integral points",

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.",

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T1 - Values of pairs involving one quadratic form and one linear form at S-integral points

AU - Lazar, Youssef

PY - 2017/12

Y1 - 2017/12

N2 - 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.

AB - 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.

KW - Quadratic forms

KW - Diophantine approximation

KW - Algebraic groups

KW - Strong approximation

KW - Ratner's Orbit Closure Theorem

U2 - 10.1016/j.jnt.2017.06.003

DO - 10.1016/j.jnt.2017.06.003

M3 - Article

SN - 0022-314X

VL - 181

SP - 200

EP - 217

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -