Open Access
VOL. 48 | 2006 Hyperelliptic curves, continued fractions, and Somos sequences
Alfred J. van der Poorten

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 212-224 (2006) DOI: 10.1214/074921706000000239


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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1221.11015
MathSciNet: MR2306202

Digital Object Identifier: 10.1214/074921706000000239

Primary: 11A55 , 11G05
Secondary: 14H05 , 14H52

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

Rights: Copyright © 2006, Institute of Mathematical Statistics

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