Metrical theorems for unconventional height functions
Number Theory
2022-07-28 v1 Dynamical Systems
Metric Geometry
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).
Cite
@article{arxiv.2202.11843,
title = {Metrical theorems for unconventional height functions},
author = {Mumtaz Hussain},
journal= {arXiv preprint arXiv:2202.11843},
year = {2022}
}
Comments
6 pages, comments welcome