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

dc.creatorHone, Andrew
dc.date2005-01-31
dc.date2006-01-30
dc.date.accessioned2026-07-07T06:39:22Z
dc.date.available2026-07-07T06:39:22Z
dc.descriptionThe 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.
dc.descriptionMore typos corrected, and extra Proposition 2.5 added. To appear in Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0501554
dc.identifierhttp://arxiv.org/abs/math/0501554
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101052
dc.subjectNumber Theory
dc.subject11B37, 33E05, 37J35
dc.titleSigma function solution of the initial value problem for Somos 5 sequences
dc.typetext

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