2015/11/30 by Yuri N. Fedorov, Fedorov, Yuri N., Andrew N. W. Hone +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Number Theory (math.NT) #math.NT #nlin.SI
paper · pdf · doi:10.48550/arxiv.1512.00056
Proof of main theorem clarified and typos corrected from version 1
arxiv created 2016/08/01 · arxiv updated 2016/08/02
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 two. For each sequence there is an associated genus two 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 four admitting an involution σ with two fixed points, and the Jacobian of X arises as the Prym variety Prym(S,σ).