Polynomial Continued Fractions for Algebraic Numbers
Henri Cohen
TL;DR
This paper proves that every real cubic algebraic number can be represented by a continued fraction with polynomial coefficients, expanding the understanding of algebraic number representations.
Contribution
It introduces a novel class of continued fractions with polynomial coefficients for algebraic numbers, specifically cubic ones.
Findings
Real cubic algebraic numbers have polynomial coefficient continued fractions
Generalizations to other algebraic numbers are discussed
Provides a new approach to algebraic number representation
Abstract
Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.
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Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals · semigroups and automata theory