Sigma function solution of the initial value problem for Somos 5 sequences

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The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.
More typos corrected, and extra Proposition 2.5 added. To appear in Trans. Amer. Math. Soc

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Number Theory, 11B37, 33E05, 37J35

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http://salesiana.dossiersoluciones.com/handle/123456789/101052

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501554
 http://arxiv.org/abs/math/0501554

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arXiv