Construction of subspaces with known Diophantine exponents for the last angle

TL;DR

This paper extends Diophantine approximation theory to subspaces of R^n, constructing specific subspaces with known exponents for the last angle using geometry of numbers.

Contribution

It provides a method to explicitly construct subspaces with computable Diophantine exponents for the last angle, generalizing classical irrationality measures.

Findings

Constructed subspaces with known Diophantine exponents

Extended Diophantine approximation to higher-dimensional subspaces

Applied geometry of numbers for explicit computations

Abstract

Schmidt generalized in 1967 the theory of classical Diophantine approximation to subspaces of $\R^n$. We consider Diophantine exponents for linear subspaces of $\R^n$ which generalize the irrationality measure for real numbers. Using geometry of numbers, we construct subspaces of $\R^n$ for which we are able to compute the associated exponents for the last angle.