On the Mixed Littlewood Conjecture and continued fractions in quadratic fields

TL;DR

This paper connects recent advances in continued fractions within quadratic fields to the classical Mixed Littlewood Conjecture, demonstrating how new results can imply longstanding conjectures.

Contribution

It establishes a link between recent results on continued fractions in quadratic fields and the classical Mixed Littlewood Conjecture, providing a new proof approach.

Findings

Recent results on continued fractions imply the Mixed Littlewood Conjecture.

The paper demonstrates the application of continued fraction evolution to number theory conjectures.

It offers a new perspective on classical problems using modern techniques.

Abstract

We show how a recent result by Aka and Shapira on the evolution of continued fractions in a fixed quadratic field implies the classic result of de Mathan and Teulli\'e on the Mixed Littlewood