On weighted inhomogeneous Diophantine approximation on planar curves

TL;DR

This paper advances the metric theory of inhomogeneous Diophantine approximation on planar curves, extending known results on measure and dimension for well-approximable points to a more general inhomogeneous setting.

Contribution

It generalizes existing homogeneous results to inhomogeneous cases for planar curves with multiple approximating functions.

Findings

Generalized Lebesgue measure results for inhomogeneous approximation

Extended Hausdorff dimension results to inhomogeneous setting

Unified framework for simultaneous inhomogeneous Diophantine approximation

Abstract

This paper develops the metric theory of simultaneous inhomogeneous Diophantine approximation on a planar curve with respect to multiple approximating functions. Our results naturally generalize the homogeneous Lebesgue measure and Hausdor? dimension results for the sets of simultaneously well-approximable points on planar curves, established in [2, 6, 10, 20].