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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. (doi:10.1112/S0024609304004163) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1112/S0024609304004163

Abstract

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
DOI/Identification number: 10.1112/S0024609304004163
Uncontrolled keywords: BACKLUND-TRANSFORMATIONS; EQUATIONS; MAPS
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 19 Dec 2007 18:25 UTC
Last Modified: 06 Feb 2020 04:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/682 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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