A zero–one law for twisted Diophantine approximation

Abstract: We study twisted Diophantine approximation, where the matrix is fixed and the target varies. I will present an exact Lebesgue measure zero–one law for arbitrary matrices and non-increasing approximation functions satisfying dyadic regularity. The criterion corrects the usual volume sum by homogeneous lattice-point counts and can be expressed through all successive minima of an associated diagonal lattice trajectory, capturing clustering in every direction. I will also discuss applications to inhomogeneous approximation constants and Hausdorff dimension. This talk is based on a joint project with Vasiliy Neckrasov; the other part establishes Hausdorff dimension formulae in uniform twisted Diophantine approximation.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar