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S-units and periodicity of continued fractions in hyperelliptic fields

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Abstract

Let L be the function field of a hyperelliptic curve defined over any field of characteristic different from 2, and let S be a set consisting of an infinite and a finite valuation of L. A relationship between the problem of the existence of nontrivial S-units in the field L and the periodicity of the continued fraction expansion of certain key elements of L is discovered for the first time for finite valuations.

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Authors and Affiliations

  1. Research Institute of System Development, Russian Academy of Sciences, Nakhimovskii pr. 36, korp. 1, Moscow, 117218, Russia

    V. P. Platonov & G. V. Fedorov

  2. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. P. Platonov

  3. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    G. V. Fedorov

Authors
  1. V. P. Platonov
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  2. G. V. Fedorov
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Corresponding author

Correspondence to V. P. Platonov.

Additional information

Original Russian Text © V.P. Platonov, G.V. Fedorov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 5, pp. 537–541.

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Platonov, V.P., Fedorov, G.V. S-units and periodicity of continued fractions in hyperelliptic fields. Dokl. Math. 92, 752–756 (2015). https://doi.org/10.1134/S1064562415060319

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  • DOI: https://doi.org/10.1134/S1064562415060319

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