Elliptic curves and quadratic recurrence sequences

Hone, Andrew N.W. (2005) Elliptic curves and quadratic recurrence sequences. Bulletin of the London Mathematical Society, 37 (Part 2). pp. 161-171. ISSN 0024-6093. (The full text of this publication is not available from this repository)

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The explicit solution of a general three-term bilinear recurrence relation of fourth order is constructed here in terms of the Weierstrass sigma function. The construction of the elliptic curve associated to the Somos 4 sequence is presented as an example. An interpretation via the theory of integrable systems is provided, leading to a conjecture relating certain higher-order recurrences with hyperelliptic curves of higher genus.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 19 Dec 2007 18:25
Last Modified: 23 Jun 2014 08:41
Resource URI: https://kar.kent.ac.uk/id/eprint/682 (The current URI for this page, for reference purposes)
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