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arXiv · 2307.10122

Rectangular shrinking targets for $\mathbb{Z}^m$ actions on tori: well and badly approximable systems

Victor Beresnevich·Shreyasi Datta·Anish Ghosh·Benjamin Ward
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Abstract

In this paper we investigate the shrinking target property for irrational rotations. This was first studied by Kurzweil (1951) and has received considerable interest of late. Using a new approach, we generalize results of Kim (2007) and Shapira (2013) by proving a weighted effective analogue of the shrinking target property. Furthermore, our results are established in the much wider $S$-arithmetic setting.

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Victor Beresnevich, Shreyasi Datta, Anish Ghosh, Benjamin Ward. 2023-07-19. Rectangular shrinking targets for $\mathbb{Z}^m$ actions on tori: well and badly approximable systems. https://arxiv.org/abs/2307.10122

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