Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
PublisherOxford University Press
Rights accessOpen Access
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).
CitationFedorov, 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.