On discrete part of Dirichlet spectrum

TL;DR

This paper extends recent advances in Diophantine approximation by analyzing the discrete part of the Dirichlet spectrum, providing new bounds and insights into approximation properties.

Contribution

It proves a new result concerning the discrete part of the Dirichlet spectrum, building on recent work related to the Lagrange spectrum.

Findings

Established bounds for the discrete part of Dirichlet spectrum.

Connected Dirichlet spectrum properties to previous Lagrange spectrum results.

Enhanced understanding of approximation quality in number theory.

Abstract

Recently J.Han\v{c}l obtained a result which improves on approximations to real numbers which correspond to the discrete part of Lagrange spectrum. In the present paper we prove a similar result related to the discrete part of Dirichlet spectrum.