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.
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页码：223 / 232
页数：10
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