Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \)

DOI10.3934/dcds.2020359zbMath1475.22028arXiv1904.02377OpenAlexW3095601214MaRDI QIDQ2030053

Jiyoung Han

Publication date: 4 June 2021

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.02377

zbMATH Keywords

Euclidean buildingquantitative Oppenheim conjecture\(S\)-arithmetic spaceaction of quadratic form-preserving groupsindefinite non-degenerate isotropic quadratic formslow-dimensional \(p\)-adic symmetric space

Mathematics Subject Classification ID

Geometric group theory (20F65) Homogeneous spaces (22F30) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Groups acting on trees (20E08) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Minima of forms (11H50) Arithmetic dynamics on general algebraic varieties (37P55)

Related Items (1)

Values of inhomogeneous forms at S ‐integral points

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equidistribution of values of linear forms on quadratic surfaces
• A quantitative Oppenheim theorem for generic diagonal quadratic forms
• Density of values of linear maps on quadratic surfaces
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
• Asymptotic distribution of values of isotropic here quadratic forms at \(S\)-integral points
• A quantitative Oppenheim theorem for generic ternary quadratic forms
• Values of random polynomials at integer points
• Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
• Raghunathan's conjectures for Cartesian products of real and \(p\)-adic Lie groups
• A generic effective Oppenheim theorem for systems of forms
• Quadratic forms of signature \((2,2)\) and eigenvalue spacings on rectangular 2-tori
• Values of pairs involving one quadratic form and one linear form at \(S\)-integral points
• Flows on \(S\)-arithmetic homogeneous spaces and applications to metric Diophantine approximation
• Approximation to algebraic numbers
• Buildings
• Oppenheim conjecture for pairs consisting of a linear form and a quadratic form
• Optimal density for values of generic polynomial maps
• Values of random polynomials in shrinking targets
• Linear algebraic groups.

This page was built for publication: Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \)