Quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms

DOI10.1215/00127094-1276319zbMath1243.11054arXiv1001.2756OpenAlexW2964141379WikidataQ123242526 ScholiaQ123242526MaRDI QIDQ541159

Amir Mohammadi, Gregory A. Margulis

Publication date: 6 June 2011

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

Full work available at URL: https://arxiv.org/abs/1001.2756

zbMATH Keywords

quadratic formDiophantineOppenheim conjecture

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) General ternary and quaternary quadratic forms; forms of more than two variables (11E20)

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Cites Work

• The quantitative behaviour of polynomial orbits on nilmanifolds
• Limit distributions of expanding translates of certain orbits on homogeneous spaces
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
• Flows on homogeneous spaces and Diophantine approximation on manifolds
• Pair correlation densities of inhomogeneous quadratic forms
• Effective equidistribution of \(S\)-integral points on symmetric varieties
• Quadratic forms of signature \((2,2)\) and eigenvalue spacings on rectangular 2-tori
• Asymptotic formulae for point lattices of bounded determinant and subspaces of bounded height
• Translate of horospheres and counting problems
• Level clustering in the regular spectrum
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