Elliptic curves and quadratic recurrence sequences

被引：37

作者：

Hone, ANW ^{[1
]}

机构：

[1] Univ Kent, Inst Math Stat & Actuarial Sci, Canterbury CT2 7NF, Kent, England

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2005年 / 37卷

关键词：

D O I：

10.1112/S0024609304004163

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：161 / 171

页数：11

共 30 条

[1]

[Anonymous], 1965, COURSE MODERN ANAL

[2]

[Anonymous], NEW YORK J MATH

[3]

Arnold VI, 2013, Mathematical methods of classical mechanics

[4] INTEGRABLE SYMPLECTIC MAPS [J].

BRUSCHI, M ;

RAGNISCO, O ;

SANTINI, PM ;

TU, GZ .

PHYSICA D, 1991, 49 (03) :273-294

[5]

BUCHSTABER VM, 1993, TEOR MAT FIZ, V94, P200

[6]

Buchstaber VM., 1997, Solitons, Geometry, and Topology: On the Crossroad, P1

[7]

CANTOR DG, 1994, J REINE ANGEW MATH, V447, P91

[8]

Dubrovin B. A., 1976, USP MAT NAUK, V31, P55

[9]

Einsiedler M., 2001, LMS Journal of Computation and Mathematics, V4

[10]

EVEREST G, 1998, HEIGHTS POLYNOMIALS

← 1 2 3 →