Badly approximable infinite products of quadratic polynomials

TL;DR

This paper establishes conditions on rational numbers u and v that guarantee the Laurent series generated by a specific infinite product of quadratic polynomials is badly approximable, contributing to number theory and Diophantine approximation.

Contribution

It introduces new criteria for the bad approximability of Laurent series derived from infinite products of quadratic polynomials.

Findings

Identifies conditions on u and v for bad approximability

Provides a framework for analyzing infinite products of quadratic polynomials

Advances understanding of Diophantine approximation in Laurent series

Abstract

We provide a number of conditions on the rational numbers $u$ and $v$ which ensure that the Laurent series $g_{u,v}(x):=\prod_{t=0}^\infty (1+ux^{-3^t} + vx^{-2\cdot 3^t})$ is badly approximable.