Values of random polynomials at integer points

DOI10.3934/jmd.2018002zbMath1454.11126arXiv1802.00792OpenAlexW2962942812MaRDI QIDQ1787202

Jayadev S. Athreya, Gregory A. Margulis

Publication date: 4 October 2018

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.00792

zbMATH Keywords

random latticesOppenheim's conjectureRogers' formula

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Lattice points in specified regions (11P21) Mean value and transfer theorems (11H60)

Related Items (15)

Explicit solutions to the Oppenheim conjecture forindefinite ternary diagonal forms ⋮ On small values of indefinite diagonal quadratic forms at integer points in at least five variables ⋮ Rogers' mean value theorem for \(S\)-arithmetic Siegel transforms and applications to the geometry of numbers ⋮ Khintchine-type theorems for values of subhomogeneous functions at integer points ⋮ 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 ⋮ Adelic Rogers integral formula ⋮ Unnamed Item ⋮ Values of random polynomials in shrinking targets ⋮ Siegel-Veech transforms are in \(L^2\) ⋮ A generic effective Oppenheim theorem for systems of forms ⋮ A quantitative Oppenheim theorem for generic ternary quadratic forms ⋮ Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \) ⋮ Distribution of values of quadratic forms at integral points

Cites Work

• Unnamed Item
• A quantitative Oppenheim theorem for generic diagonal quadratic forms
• Igusa integrals and volume asymptotics in analytic and adelic geometry
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
• Best possible rates of distribution of dense lattice orbits in homogeneous spaces
• A quantitative Oppenheim theorem for generic ternary quadratic forms
• Values at integers of homogeneous polynomials
• Logarithm laws for unipotent flows. I.
• Quadratic forms of signature \((2,2)\) and eigenvalue spacings on rectangular 2-tori
• A mean value theorem in geometry of numbers
• Random Affine Lattices
• The Number of Lattice Points in a Set
• A Metrical Theorem In Geometry of Numbers

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