Geodesic
New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields
Informatics and Automation, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 278-286 
V. P. Platonov; M. M. Petrunin. New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields. Informatics and Automation, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 278-286. http://geodesic.mathdoc.fr/item/TRSPY_2023_320_a10/
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     author = {V. P. Platonov and M. M. Petrunin},
     title = {New {Results} on the {Periodicity} {Problem} for {Continued} {Fractions} of {Elements} of {Hyperelliptic} {Fields}},
     journal = {Informatics and Automation},
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     year = {2023},
     volume = {320},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2023_320_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of describing square-free polynomials $f(x)$ of odd degree with periodic expansion of $\sqrt {f(x)}$ into a functional continued fraction in $k((x))$, where $k\subseteq \overline {\mathbb Q}$. We obtain a complete description of such polynomials $f(x)$ that does not depend on the field $k$ and the degree of a polynomial, provided that the degree $U$ of the fundamental $S$-unit of the corresponding hyperelliptic field $k(x)(\sqrt {f(x)})$ either does not exceed $12$ or is even and does not exceed $20$.

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