Diophantine Exponents of Affine Subspaces: The Simultaneous Approximation Case

TL;DR

This paper uses advanced mathematical techniques to calculate Diophantine exponents for affine subspaces and their submanifolds, enhancing understanding of simultaneous approximation in number theory.

Contribution

It introduces a novel application of nondivergence estimates to determine Diophantine exponents for affine subspaces and their nondegenerate submanifolds.

Findings

Computed Diophantine exponents for affine subspaces.

Extended results to nondegenerate submanifolds.

Provided new insights into simultaneous approximation.

Abstract

We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of $\R^n$ and their nondegenerate submanifolds.