Abstract:In this paper, we study inhomogeneous Diophantine approximation over the completion K v of a global function field K (over a finite field) for a discrete valuation v, with affine algebra R v . We obtain an effective upper bound for the Hausdorff dimension of the set}q} n }Aq ´θ ´p} m ě ǫ * , of ǫ-badly approximable targets θ P K m v for a fixed matrix A P M m,n pK v q, using an effective version of entropy rigidity in homogeneous dynamics for an appropriate diagonal action on the space of R v -grids. We furthe… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.