# On quadratic approximation for hyperquadratic continued fractions

## TL;DR

This paper investigates quadratic approximations of hyperquadratic continued fractions over finite fields, addressing Diophantine exponents and degree calculations for specific families of algebraic Laurent series.

## Contribution

It provides new insights into quadratic approximations of hyperquadratic continued fractions and answers a previously open question about Diophantine exponents.

## Key findings

- Resolved a question on Diophantine exponents for algebraic Laurent series
- Determined degrees of specific hyperquadratic continued fraction families
- Enhanced understanding of approximation properties in finite field Laurent series

## Abstract

We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the second author concerning Diophantine exponents for algebraic Laurent series. As the second application, we determine the degrees of these families in particular case.