Polynomial Continued Fractions for Algebraic Numbers

Henri Cohen

Polynomial Continued Fractions for Algebraic Numbers

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arxiv 2502.19575 v1 pith:ILACZVBC submitted 2025-02-26 math.NT

Henri Cohen This is my paper · ORCID

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keywords algebraiccontinuedpolynomialcoefficientscubicexpansionfractionfractions

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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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Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
math.NT 2026-07 conditional novelty 6.5 of 10

A theory-plus-dictionary of polynomial-type continued fractions with explicit convergence rates and Apéry-style accelerations, mostly new or newly quantified.

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