arXiv subjects

Aratrika Pandey

Publications and source records attributed to Aratrika Pandey.

2 recordsLinked to original sources

arXiv2025

Simultaneous Khintchine theorem on manifolds in positive characteristics: convergence case

We prove the convergence case of Khintchine's theorem, with general approximation functions that are not necessarily monotonic, for analytic nonplanar manifolds over local fields of positive characteristic. Our approach is based on the method of counting rational points near manifolds developed by Beresnevich and Yang. To address the scenario where the given approximating function is not monotonic, we extend our function field by adjoining an appropriate root. Additionally, in the course of the proof, we establish several new results in the geometry of numbers over function fields, which are of independent interest.

math.NT↗

arXiv2025

Exact Approximation In The Field Of Formal Series

In this article, we determine the Hausdorff dimension of the set of exactly $\psi$-approximable vectors over local fields of positive characteristic. This result is the function field analogue of a recent theorem of Bandi and de Saxc\'e in the real setting~\cite{bandi2023hausdorff}, and extends the main theorem of Zhang~\cite{MR2834892} to higher dimensions. Our approach adapts the method of Bandi and de Saxc\'e to the ultrametric setting, enabling us to overcome difficulties arising from the failure of the well-separatedness property for rational functions in higher dimensions.

math.NT↗