GENUS FIELDS OF CYCLIC l-EXTENSIONS OF RATIONAL FUNCTION FIELDS

被引：8

作者：

Bautista-Ancona, Victor ^{[1
]}

Rzedowski-Calderon, Martha ^{[2
]}

Villa-Salvador, Gabriel ^{[2
]}

机构：

[1] Univ Autonoma Yucatan, Fac Matemat, Merida, Yucatan, Mexico

[2] Ctr Invest Estudios Avanzados IPN, Dept Control Automat, Mexico City 07000, DF, Mexico

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 05期

关键词：

Genus fields; congruence function fields; global fields; Dirichlet characters; cyclotomic function fields; cyclic extensions; Kummer extensions;

D O I：

10.1142/S1793042113500243

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a construction of genus fields for Kummer cyclic l-extensions of rational congruence function fields, l a prime number. First we find this genus field for a field contained in a cyclotomic function field using Leopoldt's construction by means of Dirichlet characters and the Hilbert class field defined by Rosen. The general case follows from this. This generalizes the result obtained by Peng for a cyclic extension of degree l.

引用

页码：1249 / 1262

页数：14

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