Winning of inhomogeneous bad for curves
Number Theory
2024-11-12 v2 Dynamical Systems
Abstract
We prove the absolute winning property of weighted simultaneous inhomogeneous badly approximable vectors on non-degenerate analytic curves. This answers a question by Beresnevich, Nesharim, and Yang. In particular, our result is an inhomogeneous version of the main result in \cite{BNY22} by Beresnevich, Nesharim, and Yang. Also, the generality of the inhomogeneous part that we considered extends the previous result in \cite{ABV}. Moreover, our results even contribute to classical results, namely establishing the inhomogeneous Schmidt's conjecture in arbitrary dimensions.
Keywords
Cite
@article{arxiv.2309.02018,
title = {Winning of inhomogeneous bad for curves},
author = {Shreyasi Datta and Liyang Shao},
journal= {arXiv preprint arXiv:2309.02018},
year = {2024}
}
Comments
To appear in Math Annalen