Inhomogeneous Khintchine–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 settings, on analytic non-degenerate manifolds over a local field of positive characteristic. The dual form of Diophantine approximation has been considered here. The core of our argument is a sharp estimate for flows on homogeneous spaces, which had been originally invented in [D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds, Ann. of Math. (2) 148 1998, 1, 339–360]. 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 [9], Beresnevich, Bernik, Kleinbock and Margulis [8], Badziahin, Beresnevich and Velani [3], Mohammadi and Golsefidy [36, 37] and Datta and Ghosh [14].