Some remarks on Mahler's classification in higher dimension

TL;DR

This paper explores the metric and non-metric aspects of Mahler's classification extended to higher dimensions, applying classical Diophantine approximation results to Yu's multidimensional framework.

Contribution

It provides new insights into Mahler's classification in higher dimensions by connecting it with established Diophantine approximation theories.

Findings

Results on metric Diophantine approximation in higher dimensions

Applications of classical theorems to Yu's classification

Enhanced understanding of transcendental number classification

Abstract

We prove a number of results on the metric and non-metric theory of Diophantine approximation for Yu's multidimensional variant of Mahler's classification of transcendental numbers. Our results arise as applications of well known results in Diophantine approximation to the setting of Yu's classification.