A quantitative Oppenheim theorem for generic diagonal quadratic forms

DOI10.1007/s11856-016-1385-7zbMath1361.11024arXiv1604.02087OpenAlexW2962961858MaRDI QIDQ502993

Jean Bourgain

Publication date: 11 January 2017

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

Full work available at URL: https://arxiv.org/abs/1604.02087

zbMATH Keywords

indefinite ternary quadratic formsOppenheim's conjecture

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) General ternary and quaternary quadratic forms; forms of more than two variables (11E20)

Related Items (17)

Explicit solutions to the Oppenheim conjecture forindefinite ternary diagonal forms ⋮ Density of rational points near/on compact manifolds with certain curvature conditions ⋮ On small values of indefinite diagonal quadratic forms at integer points in at least five variables ⋮ Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori ⋮ Khintchine-type theorems for values of subhomogeneous functions at integer points ⋮ Values of inhomogeneous forms at S ‐integral points ⋮ Inhomogeneous Diophantine approximation for generic homogeneous functions ⋮ Finitary analysis in homogeneous spaces ⋮ 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 ⋮ A generic effective Oppenheim theorem for systems of forms ⋮ Small gaps in the spectrum of the rectangular billiard ⋮ A quantitative Oppenheim theorem for generic ternary quadratic forms ⋮ Values of random polynomials at integer points ⋮ Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \) ⋮ On the kinetic wave turbulence description for NLS ⋮ Distribution of values of quadratic forms at integral points

Cites Work

• Effective estimates on indefinite ternary forms
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
• Zero-density estimates for L-functions
• Small gaps in the spectrum of the rectangular billiard
• EPSTEIN ZETA-FUNCTIONS, SUBCONVEXITY, AND THE PURITY CONJECTURE
• Shrinking targets for semisimple groups
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