Elliptic curves and continued fractions

Abstract

We detail the continued fraction expansion of the square root of the general monic quartic polynomial, noting that each line of the expansion corresponds to addition of the divisor at infinity. We analyse the data yielded by the general expansion. In that way we obtain `elliptic sequences' satisfying Somos relations. I mention several new results on such sequences. The paper includes a detailed `reminder exposition' on continued fractions of quadratic irrationals in function fields.

v1; final -- I hope

Cited by in corpus (5)

• Laurent Polynomials and Superintegrable Maps
• Integrality and the Laurent phenomenon for Somos 4 sequences
• Genus 2 curves, continued fractions, and Somos sequences
• Sigma function solution of the initial value problem for Somos 5 sequences
• Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials