Some manifolds of Khinchin type for convergence

TL;DR

This paper enhances existing methods to establish stronger Khinchin-type convergence results for manifolds, improving upon recent and classical theorems in metric number theory.

Contribution

It refines and optimizes techniques for proving Khinchin-type convergence on manifolds, strengthening previous results and extending their applicability.

Findings

Stronger conditions for Khinchin-type convergence on manifolds.

Improved theorem of Dodson, Rynne, and Vickers ('89).

More optimal use of existing techniques.

Abstract

Recently, Beresnevich, Vaughan, Velani, and Zorin (arXiv: 1506.09049) gave some sufficient conditions for a manifold to be of Khinchin type for convergence. We show that their techniques can be used in a more optimal way to yield stronger results. In the process we also improve a theorem of Dodson, Rynne, and Vickers ('89).