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Hyperelliptic curves, continued fractions, and Somos sequences

2006/08/10 by Alfred J. van der Poorten · 1 citation
Mathematics · #math.NT #math.AG #msc:11A55 #msc:11G05 #msc:14H05 #msc:14H52

paper · pdf · doi:10.1214/074921706000000239

published as IMS Lecture Notes--Monograph Series 2006, Vol. 48, 212-224 · Published 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)

arxiv created 2006/08/10 · arxiv updated 2009/12/01

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.

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