Oppenheim conjecture for pairs consisting of a linear form and a quadratic form

DOI10.1090/S0002-9947-04-03473-7zbMath1051.11034arXivmath/0310231WikidataQ123277669 ScholiaQ123277669MaRDI QIDQ4813856

Alexander Gorodnik

Publication date: 13 August 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310231

zbMATH Keywords

quadratic formergodicitystabilizerlinear formunipotent pair

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Simultaneous homogeneous approximation, linear forms (11J13) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Homogeneous flows (37A17)

Related Items (9)

On an Oppenheim-type conjecture for systems of quadratic forms ⋮ Values of pairs involving one quadratic form and one linear form at \(S\)-integral points ⋮ Khintchine-type theorems for values of subhomogeneous functions at integer points ⋮ Inhomogeneous Diophantine approximation for generic homogeneous functions ⋮ On the density at integer points of a system comprising an inhomogeneous quadratic form and a linear form ⋮ Systems of quadratic Diophantine inequalities and the value distribution of quadratic forms ⋮ A generic effective Oppenheim theorem for systems of forms ⋮ Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \) ⋮ Density of values of linear maps on quadratic surfaces

Cites Work

• Raghunathan's topological conjecture and distributions of unipotent flows
• Uniformly distributed orbits of certain flows on homogeneous spaces
• Orbit closures of generic unipotent flows on homogeneous spaces of \(SL(3,{\mathbb{R}})\)
• Values of quadratic forms at primitive integral points
• Values of indefinite quadratic forms at integral points and flows on spaces of lattices
• Unnamed Item

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