Quantitative Version of the Oppenheim Conjecture for Inhomogeneous Quadratic Forms
G. A. Margulis, A. Mohammadi
TL;DR
This paper proves a quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms and applies it to eigenvalue spacing problems on flat 2-tori with Aharonov-Bohm flux.
Contribution
It introduces a quantitative approach to the Oppenheim conjecture for inhomogeneous quadratic forms and connects it to spectral properties of flat tori with magnetic flux.
Findings
Quantitative bounds for inhomogeneous quadratic forms
Application to eigenvalue spacing on flat 2-tori
Insights into spectral theory with magnetic flux
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.
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