On the Jacobians of Curves Defined by the Generalized Laguerre Polynomials

被引：1

作者：

Cullinan, John ^{[1
]}

机构：

[1] Bard Coll, Math, Annandale On Hudson, NY 12504 USA

来源：

EXPERIMENTAL MATHEMATICS | 2019年 / 28卷 / 02期

关键词：

algebraic curve; galois representation; orthogonal polynomial; REPRESENTATIONS; FAMILY; GENUS;

D O I：

10.1080/10586458.2017.1382405

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be the nth Generalized Laguerre Polynomial. In this paper we study the arithmetic of the algebraic curves defined by L-n(⟨alpha⟩)(x) = 0, viewed as a two-variable polynomial over Q, and their Jacobians . We introduce a conjecture for the endomorphism ring, Mordell-Weil group, and image of the l-adic representations of the for all n >= 4.

引用

页码：223 / 232

页数：10

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