Algebraic curves, integer sequences and a discrete Painleve transcendent

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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 Painlevé I equation are briefly considered.
Poster at SIDE 6, Helsinki, Finland, 19-24 June 2004. One reference and some numerical values have been updated. The conjecture on p.6 is wrong

Keywords

Exactly Solvable and Integrable Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/165034

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.2538
 http://arxiv.org/abs/0807.2538

Collections

arXiv