Inhomogeneous Khitchine-Groshev type theorems on manifolds over function fields

TL;DR

This paper establishes a comprehensive Khintchine-Groshev theorem for Diophantine approximation on analytic manifolds over function fields of positive characteristic, extending classical results to a new algebraic setting.

Contribution

It provides the first complete inhomogeneous and homogeneous Khintchine-Groshev theorems over function fields, generalizing previous Euclidean and S-adic results to positive characteristic fields.

Findings

Proves a Khintchine-Groshev theorem in the function field setting.

Extends Diophantine approximation results to nondegenerate manifolds over local fields.

Includes dual form analysis of Diophantine approximation in this context.

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.