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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 516, Pages 59–64
DOI: https://doi.org/10.31857/S2686954324020093 (Mi danma513) 		 
MATHEMATICS

Continued fractions in hyperelliptic fields with an arbitrarily long period

V. P. Platonovab, G.V. Fedorovac

a Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c University of Science and Technology "Sirius", Sochi
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DOI: https://doi.org/10.31857/S2686954324020093
Abstract: The article proves the following statement: in any hyperelliptic field $L$ defined over the field of algebraic numbers $K$ which having non-trivial units of the ring of integer elements of the field $L$, there is an element for which the period length of the continued fraction is greater any pre-given number.
Keywords: hyperelliptic field, fundamental units, unimodular transformations, period length.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FNEF-2024-0001
This work was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the state assignment, project no. FNEF-2024-0001.
Received: 15.02.2024
Revised: 25.03.2024
Accepted: 25.03.2024
English version:
Doklady Mathematics, 2024, Volume 109, Issue 2, Pages 147–151
DOI: https://doi.org/10.1134/S1064562424701928
Bibliographic databases:
Document Type: Article
UDC: 511.6
Language: Russian
Citation: V. P. Platonov, G.V. Fedorov, “Continued fractions in hyperelliptic fields with an arbitrarily long period”, Dokl. RAN. Math. Inf. Proc. Upr., 516 (2024), 59–64; Dokl. Math., 109:2 (2024), 147–151
Citation in format AMSBIB
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\by V.~P.~Platonov, G.V.~Fedorov
\paper Continued fractions in hyperelliptic fields with an arbitrarily long period
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 516
\pages 59--64
\mathnet{http://mi.mathnet.ru/danma513}
\crossref{https://doi.org/10.31857/S2686954324020093}
\elib{https://elibrary.ru/item.asp?id=68623165}
\transl
\jour Dokl. Math.
\yr 2024
\vol 109
\issue 2
\pages 147--151
\crossref{https://doi.org/10.1134/S1064562424701928}
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