Hone, Andrew N.W. (2008) Algebraic curves, integer sequences and a discrete Painleve transcendent. In: SIDE 6, 1924 June 2004, Helsinki, Finland. (Unpublished)
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Official URL http://arxiv.org/abs/0807.2538 
Abstract
We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general threeterm bilinear recurrence relation of fourth order is given in terms of the Weierstrass sigma function for an associated elliptic curve. The recurrences can generate integer sequences, including the Somos 4 sequence and elliptic divisibility sequences. An interpretation via the theory of integrable systems suggests the relation between certain higher order recurrences and hyperelliptic curves of higher genus. Analogous sequences associated with a qdiscrete Painlev\'e I equation are briefly considered.
Item Type:  Conference or workshop item (Poster) 

Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory Q Science > QA Mathematics (inc Computing science) > QA351 Special functions 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science 
Depositing User:  Andrew N W Hone 
Date Deposited:  21 Jun 2014 00:25 UTC 
Last Modified:  29 May 2019 12:41 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/41489 (The current URI for this page, for reference purposes) 
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