Hyperelliptic curves, continued fractions, and Somos sequences

Details Hyperelliptic curves, continued fractions, and Somos sequences Hyperelliptic curves, continued fractions, and Somos sequences

2006-08-10

arxiv.org/abs/math/0608247v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 212-224

Mathematics

Number Theory

Published at http://dx.doi.org/10.1214/074921706000000239 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

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.

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