Optimal density for values of generic polynomial maps

DOI10.1353/ajm.2020.0049zbMath1498.11168arXiv1801.01027OpenAlexW3101380633MaRDI QIDQ5147272

Anish Ghosh, Alexander Gorodnik, Amos Nevo

Publication date: 3 February 2021

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.01027

zbMATH Keywords

semisimple Lie groupOppenheim Diophantine approximation problempigeonhole lower bound

Mathematics Subject Classification ID

Homogeneous spaces (22F30) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Diophantine approximation in probabilistic number theory (11K60) Homogeneous flows (37A17)

Related Items (8)

Explicit solutions to the Oppenheim conjecture forindefinite ternary diagonal forms ⋮ Rogers' mean value theorem for \(S\)-arithmetic Siegel transforms and applications to the geometry of numbers ⋮ Values of inhomogeneous forms at S ‐integral points ⋮ Second moment of the light-cone Siegel transform and applications ⋮ 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 ⋮ Values of random polynomials in shrinking targets ⋮ Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \)

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