Determined Sequences, Continued Fractions, and Hyperelliptic Curves

In this report I sanitise (in the sense of `bring some sanity to') the arguments of earlier reports detailing the correspondence between sequences (M +hS)-<h< of divisors on elliptic and genus two hyperelliptic curves, the continued fraction expansion of quadratic irrational functions in the relevant elliptic and hyperelliptic function fields, and certain integer sequences satisfying relations of Somos type. I note that one may often readily determine the coefficients in those relations by elementary linear algebra. I begin with some musings on here called `determined sequences', and continue with detail on continued fraction expansion of square roots of polynomials and associated Somos type sequences particularly in the genus 1 and 2 cases. 1 Remarks on Determined Sequences

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: Alfred J. van der Poorten
• Keywords: Algorithms, ANTS 2006, Continued Fraction Expansion, Sequences Satisfying Relations, Somos Type