Representations of integers by an invariant polynomial and unipotent flows

DOI10.1215/S0012-7094-06-13533-0zbMath1138.11011arXivmath/0409506OpenAlexW2142309744MaRDI QIDQ860112

Alex Eskin, Hee Oh

Publication date: 23 January 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409506

zbMATH Keywords

homogeneous polynomialDiophantineunipotent flowssemisimple real algebraic group

Mathematics Subject Classification ID

Related Items (13)

Equidistribution of Hodge loci II ⋮ On the equidistribution of some Hodge loci ⋮ Effective equidistribution of \(S\)-integral points on symmetric varieties ⋮ Linnik's problem in fiber bundles over quadratic homogeneous varieties ⋮ Finitary analysis in homogeneous spaces ⋮ Distribution of periodic torus orbits and Duke's theorem for cubic fields ⋮ Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows ⋮ Local-global principles for representations of quadratic forms ⋮ Rational points on homogeneous varieties and equidistribution of adelic periods (with appendix by Mikhail Borovoi) ⋮ Effective equidistribution and property (𝜏) ⋮ Distribution of periodic torus orbits on homogeneous spaces ⋮ Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces ⋮ Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-divergence of translates of certain algebraic measures
• Arithmetic subgroups of algebraic groups
• Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces
• Raghunathan's topological conjecture and distributions of unipotent flows
• Fourier coefficients of modular forms of half-integral weight
• Hyperbolic distribution problems and half-integral weight Maass forms
• Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
• On Raghunathan's measure conjecture
• Mixing, counting, and equidistribution in Lie groups
• Hardy-Littlewood system and representations of integers by an invariant polynomial
• Group schemes and local densities.
• Unipotent flows and counting lattice points on homogeneous varieties
• A New Application of the Hardy-Littlewood-Kloosterman Method
• On the space of ergodic invariant measures of unipotent flows
• Values of indefinite quadratic forms at integral points and flows on spaces of lattices
• Hecke operators and equidistribution of Hecke points

This page was built for publication: Representations of integers by an invariant polynomial and unipotent flows