# Quadratic Lagrange spectrum: I

## TL;DR

This paper establishes the existence of Hall's ray for quadratic Lagrange spectra of all real quadratic numbers and computes Hurwitz constants for many such spectra, advancing understanding of Diophantine approximation.

## Contribution

It proves the existence of Hall's ray for quadratic Lagrange spectra and calculates Hurwitz constants for a broad class of real quadratic numbers, a novel extension in the field.

## Key findings

- Hall's ray exists for all real quadratic numbers' spectra
- Hurwitz constants are computed for many quadratic Lagrange spectra
- Provides new insights into Diophantine approximation of quadratic irrationals

## Abstract

In this paper we prove the existence of Hall's ray for the quadratic Lagrange spectrums of all real quadratic numbers. For a large class of real quadratic numbers, we compute the Hurwitz constants of their quadratic Lagrange spectrums