Fedorov, Yuri N., Hone, Andrew N.W. (2016) Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties. Journal of Integrable Systems, 1 (1). ISSN 2058-5985. (doi:10.1093/integr/xyw012) (KAR id:53527)
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Official URL: https://doi.org/10.1093/integr/xyw012 |
Abstract
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 \(\sigma\) with two fixed points, and the Jacobian of \(X\) arises as the Prym variety Prym \((S,\sigma)\).
Item Type: | Article |
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DOI/Identification number: | 10.1093/integr/xyw012 |
Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory Q Science > QA Mathematics (inc Computing science) > QA351 Special functions Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic Geometry |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Andrew Hone |
Date Deposited: | 18 Dec 2015 12:52 UTC |
Last Modified: | 17 Aug 2022 12:20 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/53527 (The current URI for this page, for reference purposes) |
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