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 <nobr>$S$</nobr>-units of degree at most 11”, Dokl. RAN. Math. Inf. Proc. Upr., 2021, Volume 500,Pages <nobr>45

This article is cited in 2 papers

MATHEMATICS

On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental $S$-units of degree at most 11

V. P. Platonov^ab, M. M. Petrunin^a, Yu. N. Shteinikov^a

^a Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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.

UDC: 511.6

Received: 26.08.2021
Revised: 26.08.2021
Accepted: 01.09.2021

DOI: 10.31857/S2686954321050088