Institute of Mathematical Statistics Lecture Notes - Monograph Series

Hyperelliptic curves, continued fractions, and Somos sequences

Alfred J. van der Poorten

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Abstract

We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. In the quartic and sextic cases we observe explicitly that the parameters appearing in the continued fraction expansion yield integer sequences defined by bilinear relations instancing sequences of Somos type.

Chapter information

Source
Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 212-224

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285822

Digital Object Identifier
doi:10.1214/074921706000000239

Mathematical Reviews number (MathSciNet)
MR2306202

Zentralblatt MATH identifier
1221.11015

Subjects
Primary: 11A55: Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 14H05: Algebraic functions; function fields [See also 11R58] 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx]

Keywords
continued fraction expansion function field of characteristic zero hyperelliptic curve Somos sequence

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

van der Poorten, Alfred J. Hyperelliptic curves, continued fractions, and Somos sequences. Dynamics & Stochastics, 212--224, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000239. https://projecteuclid.org/euclid.lnms/1196285822


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