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Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties

Autor
Fedorov, Y.; Hone, A.
Tipus d'activitat
Article en revista
Revista
Journal of Integrable Systems
Data de publicació
2016-09-09
Volum
1
Pàgina inicial
1
Pàgina final
34
DOI
https://doi.org/10.1093/integr/xyw012 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/105044 Obrir en finestra nova
Resum
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 ...
Citació
Fedorov, 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.
Paraules clau
Lax represetation, Prym varieties, general Somos-6 recurrence, sigma function solution
Grup de recerca
SD - Sistemes Dinàmics de la UPC

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