On a particular hyperquadratic continued fraction in F(p) with p>2

TL;DR

This paper explores a specific hyperquadratic continued fraction in the field of power series over a finite field, providing explicit algebraic equations and connecting to historical algebraic continued fractions.

Contribution

It introduces a new hyperquadratic continued fraction in F(p) with explicit algebraic equations and links to earlier work by Mills and Robbins.

Findings

Explicit algebraic equations for the continued fraction.

Connection established with historical algebraic continued fractions.

Provides detailed description of the continued fraction in F(p).

Abstract

Given an odd prime number p, we describe a continued fraction in the field F(p) of power series in 1/T with coefficients in the finite field F_p, where T is a formal indeterminate. This continued fraction satisfies an algebraic equation of a particular type, with coefficients in F_p[T] which are explicitely given. We observe the close connection with other algebraic continued fractions studied thirty years ago by Mills and Robbins.