Hyperelliptic curves, continued fractions, and Somos sequences
Number Theory
2007-05-23 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0608247,
title = {Hyperelliptic curves, continued fractions, and Somos sequences},
author = {Alfred J. van der Poorten},
journal= {arXiv preprint arXiv:math/0608247},
year = {2007}
}
Comments
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)