Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.4

Curves of Genus 2, Continued Fractions, and Somos Sequences

Alfred J. van der Poorten
Centre for Number Theory Research
1 Bimbil Place
Killara, Sydney
NSW 2071
Australia

Abstract: 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 width 6.

Received November 12 2004; revised version received July 21 2005. Published in Journal of Integer Sequences July 28 2005.