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

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