Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
Tipus de documentArticle
EditorOxford University Press
Condicions d'accésAccés obert
We construct the explicit solution of the initial value problem for sequences generated by the general Somos-6 recurrence relation, in terms of the Kleinian sigma-function of genus 2. For each sequence there is an associated genus 2 curve X, such that iteration of the recurrence corresponds to translation by a fixed vector in the Jacobian of X. The construction is based on a Lax pair with a spectral curve S of genus 4 admitting an involution s with two fixed points, and the Jacobian of X arises as the Prym variety Prym(S,s).
CitacióFedorov, Y., Hone, A. Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties. "Journal of Integrable Systems", 9 Setembre 2016, vol. 1, p. 1-34.