Quantitative Diophantine approximation on affine subspaces
Arijit Ganguly, Anish Ghosh
TL;DR
This paper extends recent results on Diophantine approximation from nondegenerate manifolds to affine subspaces, providing quantitative bounds relevant to applications like interference alignment.
Contribution
It develops analogues of the Khintchine-Groshev theorem for affine subspaces, advancing the understanding of Diophantine approximation in these settings.
Findings
Established quantitative approximation results for affine subspaces
Extended Khintchine-Groshev type theorems to affine subspaces
Provided tools for applications in interference alignment
Abstract
Recently, Adiceam, Beresnevich, Levesley, Velani and Zorin proved a quantitative version of the convergence case of the Khintchine-Groshev theorem for nondegenerate manifolds, motivated by applications to interference alignment. In the present paper, we obtain analogues of their results for affine subspaces.
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