Hyperelliptic curves, continued fractions, and Somos sequences

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dc.creatorvan der Poorten, Alfred J.
dc.date2006-08-10
dc.date.accessioned2026-07-07T07:21:36Z
dc.date.available2026-07-07T07:21:36Z
dc.descriptionWe 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/074921706000000239 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0608247
dc.identifierhttp://arxiv.org/abs/math/0608247
dc.identifierIMS Lecture Notes--Monograph Series 2006, Vol. 48, 212-224
dc.identifierdoi:10.1214/074921706000000239
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115359
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11A55, 11G05 (Primary) 14H05, 14H52 (Secondary)
dc.titleHyperelliptic curves, continued fractions, and Somos sequences
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