Inhomogeneous Khitchine-Groshev type theorems on manifolds over function fields

Abstract

The goal of this paper is to establish a complete Khintchine-Groshev type theorem in both homogeneous and inhomogeneous setting, on analytic nondegenerate manifolds over a local field of positive characteristic. The dual form of Diophantine approximation has been considered here. Our treatise provides the function field analogues of the various earlier results of this type, studied in the euclidean and S-adic framework, by Bernik, Kleinbock and Margulis, Beresnevich, Bernik, Kleinbock and Margulis, Badziahin, Beresnevich and Velani, Mohammadi and Golsefidy, and Datta and Ghosh.