Metrical theorems for unconventional height functions

Mumtaz Hussain

doi:10.1016/j.jmaa.2022.126454

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arXiv · 2202.11843

Metrical theorems for unconventional height functions

Mumtaz Hussain

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Abstract

In this paper, we consider the simultaneous approximation of real points by rational points with the error of approximation given by the functions of `non-standard' heights. We prove analogues of Khintchine and Jarn\'ik-Besicovitch theorems for this setting, thus answering some questions raised by Fishman and Simmons (2017).

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Mumtaz Hussain. 2022-02-24. Metrical theorems for unconventional height functions. https://doi.org/10.1016/j.jmaa.2022.126454

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