Genus 2 curves, continued fractions, and Somos sequences

Details Genus 2 curves, continued fractions, and Somos sequences Genus 2 curves, continued fractions, and Somos sequences

2004-12-19

arxiv.org/abs/math/0412372v1

Mathematics

Number Theory

6 pages

Scientific paper

We detail the continued fraction expansion of the square root of monic sextic
polynomials. We note in passing that each line of the expansion corresponds to
addition of the divisor at infinity, and interpret the data yielded by the
general expansion. In particular we obtain an associated Somos sequence defined
by a three-term recurrence relation of gap~6.

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