Explicit formulas for Drinfeld modules and their periods

被引：15

作者：

El-Guindy, Ahmad ^{[1
,2
]}

Papanikolas, Matthew A. ^{[3
]}

机构：

[1] Texas A&M Univ Qatar, Sci Program, Doha, Qatar

[2] Cairo Univ, Dept Math, Fac Sci, Giza 12613, Egypt

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 06期

基金：

美国国家科学基金会;

关键词：

Drinfeld modules; Exponentials; Logarithms; Periods; Supersingularity;

D O I：

10.1016/j.jnt.2012.10.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well-known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1864 / 1886

页数：23

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