Geodesic
On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental $S$-units of degree at most 11
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 45-51

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We solve the problem of describing square-free polynomials $f(x)\in k[x]$ with a periodic expansion of $\sqrt{f(x)}$ into a functional continued fraction in $k((x))$, where $k$ is a number field and the degree of the corresponding fundamental $S$-unit of the hyperelliptic field $k(x)(\sqrt{f(x)})$ is less than or equal to 11.
Keywords: hyperelliptic field, $S$-units, continued fractions, periodicity, torsion points. 
@article{DANMA_2021_500_a8,
     author = {V. P. Platonov and M. M. Petrunin and Yu. N. Shteinikov},
     title = {On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental $S$-units of degree at most 11},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {45--51},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a8/}
}
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V. P. Platonov; M. M. Petrunin; Yu. N. Shteinikov. On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental $S$-units of degree at most 11. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 45-51. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a8/