Quantitative Version of the Oppenheim Conjecture for Inhomogeneous Quadratic Forms

Abstract

A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.

Cited by in corpus (10)

• An Effective Ratner Equidistribution Result for ASL(2,R)
• Effective density for inhomogeneous quadratic forms I: generic forms and fixed shifts
• Pair correlation for quadratic polynomials mod 1
• Khintchine-type theorems for values of subhomogeneous functions at integer points
• An effective equidistribution result for $SL(2,R)⋉(R^2{)}^{\oplus k}$ and application to inhomogeneous quadratic forms
• Waring's problem with shifts
• Sums of cubes with shifts
• Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit
• Quantum Transport in a Low-Density Periodic Potential: Homogenisation via Homogeneous Flows
• Some new results in quantitative Diophantine approximation