Khintchine's theorem for affine hyperplanes in positive charateristic

Abstract

In this paper we establish the convergence case of Khintchine's theorem for affine hyperplanes in function field of positive characteristic. Along with that, we also prove a quantitative version of the same. The main technique used in the proof is a dynamical result called 'Quantitative nondivergence' due to D. Y. Kleinbock and G. A. Margulis [17].