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Algebraic curves, integer sequences and a discrete Painleve transcendent

Hone, Andrew N.W. (2008) Algebraic curves, integer sequences and a discrete Painleve transcendent. In: SIDE 6, 19-24 June 2004, Helsinki, Finland. (Unpublished) (KAR id:41489)


We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general three-term 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 q-discrete 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: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 21 Jun 2014 00:25 UTC
Last Modified: 16 Nov 2021 10:16 UTC
Resource URI: (The current URI for this page, for reference purposes)

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